RS Aggarwal solutions for Mathematics [English] Class 6 chapter 2 - Factors and Multiples [Latest edition]

Define: (i) factor (ii) multiple. Give five examples of each.

Write down the factors of 20.

Write down the factors of 36.

Write down the factors of 60.

Write down the factors of 75.

Write the first five multiples of the following number:
17

Write the first five multiples of the following number:
23

Write the first five multiples of the following number:
65

Write the first five multiples of the following number:
70

State if the following number is even or odd.
32

State if the following number is even or odd.
37

State if the following number is even or odd.
50

State if the following number is even or odd.
58

State if the following number is even or odd.
69

State if the following number is even or odd.
144

State if the following number is even or odd.
144

State if the following number is even or odd.
321

State if the following number is even or odd.
253

What are prime numbers? Give ten examples.

Write all the prime numbers between:
10 and 40

Write all the prime numbers between:
80 and 100

Write all the prime numbers between:
40 and 80

Write all the prime numbers between:
30 and 40

Write the smallest prime number.

List all even prime numbers.

Write the smallest odd prime number.

Find if the following number is a prime number:
87

Find if the following number is a prime number:
89

Find if the following number is a prime number:
63

Find if the following number is a prime number:
91

Make a list of seven consecutive numbers, none of which is prime.

Is there any counting number having no factor at all?

Find all the numbers having exactly one factor.

Find numbers between 1 and 100 having exactly three factors.

What are composite numbers? Can a composite number be odd? If yes, write the smallest odd composite number.

What are twin primes?
Write all the pairs of twin primes between 50 and 100

What are co-primes?

Give examples of five pairs of co-primes.

Are co-primes always primes? If no, illustrate your answer by an example.

Express the following number as the sum of two odd prime:
36

Express the following number as the sum of two odd prime:
42

Express the following number as the sum of two odd prime:
84

Express the following number as the sum of two odd prime:
98

Express the following odd number as the sum of three odd prime number:
31

Express the following odd number as the sum of three odd prime number:
35

Express the following odd number as the sum of three odd prime number:
49

Express the following odd number as the sum of three odd prime number:
63

Express the following number as the sum of twin prime:
36

Express the following number as the sum of twin prime:
84

Express the following number as the sum of twin prime:
120

Express the following number as the sum of twin prime:
144

State the following statement is True or False.
1 is the smallest prime number.

State the following statement is True or False.
 If a number is prime, it must be odd.

State the following statement is True or False.
The sum of two prime numbers is always a prime number.

State the following statement as True or False.

If two numbers are co-primes, at least one of them must be a prime number.

Test the divisibility of the following number by 2:
2650

Test the divisibility of the following number by 2:
69435

Test the divisibility of the following number by 2:
59628

Test the divisibility of the following number by 2:
789403

Test the divisibility of the following number by 2:
357986

Test the divisibility of the following number by 2:
367314

Test the divisibility of the following number by 3:
733

Test the divisibility of the following number by 3:
10038

Test the divisibility of the following number by 3:
20701

Test the divisibility of the following number by 3:
524781

Test the divisibility of the following number by 3:
79124

Test the divisibility of the following number by 3:
872645

Test the divisibility of the following number by 4:

618

Test the divisibility of the following number by 4:

2314

Test the divisibility of the following number by 4:

63712

Test the divisibility of the following number by 4:

35056

Test the divisibility of the following number by 4:

946126

Test the divisibility of the following number by 4:

810524

Test the divisibility of the following numbers by 5:

4965

Test the divisibility of the following numbers by 5:

23590

Test the divisibility of the following numbers by 5:

35208

Test the divisibility of the following numbers by 5:

723405

Test the divisibility of the following numbers by 5:

124684

Test the divisibility of the following numbers by 5:

438750

Test the divisibility of the following numbers by 6:

2070

Test the divisibility of the following numbers by 6:

46523

Test the divisibility of the following numbers by 6:

71232

Test the divisibility of the following numbers by 6:

934706

Test the divisibility of the following numbers by 6:

251780

Test the divisibility of the following numbers by 6:

872536

Test the divisibility of the following numbers by 7:

826

Test the divisibility of the following numbers by 7:

117

Test the divisibility of the following numbers by 7:

2345

Test the divisibility of the following numbers by 7:

6021

Test the divisibility of the following numbers by 7:

14126

Test the divisibility of the following numbers by 7:

25368

Test the divisibility of the following numbers by 8:

9364

Test the divisibility of the following numbers by 8:

2138

Test the divisibility of the following numbers by 8:

36792

Test the divisibility of the following numbers by 8:

901674

Test the divisibility of the following numbers by 8:

136976

Test the divisibility of the following numbers by 8:

1790184

Test the divisibility of the following numbers by 9:

2358

Test the divisibility of the following numbers by 9:

3333

Test the divisibility of the following numbers by 9:

98712

Test the divisibility of the following numbers by 9:

257106

Test the divisibility of the following numbers by 9:

647514

Test the divisibility of the following numbers by 9:

326999

Test the divisibility of the following number by 10:

5790

Test the divisibility of the following number by 10:

63215

Test the divisibility of the following number by 10:

55555

Test the divisibility of the following number by 11:

4334

Test the divisibility of the following number by 11:

83721

Test the divisibility of the following number by 11:

66311

Test the divisibility of the following number by 11:

137269

Test the divisibility of the following number by 11:

901351

Test the divisibility of the following number by 11:

8790322

In the following number, replace * by the smallest number to make it divisible by 3:

 27*4

In the following number, replace * by the smallest number to make it divisible by 3:

53*46

In the following number, replace * by the smallest number to make it divisible by 3:

8*711

In the following number, replace * by the smallest number to make it divisible by 3:

62*35

In the following number, replace * by the smallest number to make it divisible by 3:

234*17

In the following number, replace * by the smallest number to make it divisible by 3:

6*1054

In the following number, replace * by the smallest number to make it divisible by 9:

65*5

In the following number, replace * by the smallest number to make it divisible by 9:

2*135

In the following number, replace * by the smallest number to make it divisible by 9:

6702*

In the following number, replace * by the smallest number to make it divisible by 9:

91*67

In the following number, replace * by the smallest number to make it divisible by 9:

6678*1

In the following number, replace * by the smallest number to make it divisible by 9:

835*86

In the following number, replace * by the smallest number to make it divisible by 11:

26*5

In the following number, replace * by the smallest number to make it divisible by 11:

39*43

In the following number, replace * by the smallest number to make it divisible by 11:

86*72

In the following number, replace * by the smallest number to make it divisible by 11:

467*91

In the following number, replace * by the smallest number to make it divisible by 11:

1723*4

In the following number, replace * by the smallest number to make it divisible by 11:

9*8071

Test the divisibility of 1000001 by 11.

Test the divisibility of 19083625 by 11.

Test the divisibility of 2134563 by 9.

Test the divisibility of 10001001 by 3.

Test the divisibility of 10203574 by 4.

Test the divisibility of 12030624 by 8.

State if the following is a prime number?

103

State if the following is a prime number?

137

State if the following is a prime number?

161

State if the following is a prime number?

179

State if the following is a prime number?

217

State if the following is a prime number?

277

State if the following is a prime number?

331

State if the following is a prime number?

397

Give an example of a number which is divisible by 2 but not by 4.

Give an example of a number which is divisible by 4 but not by 8.

Give an example of a number which is divisible by both 2 and 8 but not by 16.

Give an example of a number which is divisible by both 3 and 6 but not by 18.

Write (T) for true and (F) for false against the following statement:

If a number is divisible by 4, it must be divisible by 8.

Write (T) for true and (F) for false against the following statement:

If a number is divisible by 8, it must be divisible by 4.

Write (T) for true and (F) for false against the following statement:

If a number divides the sum of two numbers exactly, it must exactly divide the numbers separately.

Write (T) for true and (F) for false against the following statement:

If a number is divisible by both 9 and 10, it must be divisible by 90.

Write (T) for true and (F) for false against the following statement:

A number is divisible by 18 if it is divisible by both 3 and 6.

Write (T) for true and (F) for false against the following statement:

If a number is divisible by 3 and 7, it must be divisible by 21.

Write (T) for true and (F) for false against the following statement:

The sum of two consecutive odd numbers is always divisible by 4.

Write (T) for true and (F) for false against the following statement:

If a number divides two numbers exactly, it must divide their sum exactly.

Give the prime factorization of the following number:
12

Give the prime factorization of the following number:
18

Give the prime factorization of the following number:
48

Give the prime factorization of the following number:
56

Give the prime factorization of the following number:

Give the prime factorization of the following number:

Give the prime factorization of the following number:

Give the prime factorization of the following number:

Give the prime factorization of the following number:

Give the prime factorization of the following number:

Give the prime factorization of the following number:

Give the prime factorization of the following number:

Give the prime factorization of the following number:

Give the prime factorization of the following number:

Give the prime factorization of the following number:

Give the prime factorization of the following number:

Give the prime factorization of the following number:

Give the prime factorization of the following number:

Give the prime factorization of the following number:

Give the prime factorization of the following number:

Find the HCF of the numbers in each of the following, using the prime factorization method:
84, 98

Find the HCF of the numbers in each of the following, using the prime factorization method:
170, 238

Find the HCF of the numbers in each of the following, using the prime factorization method:
504, 980

Find the HCF of the numbers in each of the following, using the prime factorization method:
72, 108, 180

Find the HCF of the numbers in each of the following, using the prime factorization method:
84, 120, 138

Find the HCF of the numbers in each of the following, using the prime factorization method:
106, 159, 371

Find the HCF of the numbers in each of the following, using the prime factorization method:
272, 425

Find the HCF of the numbers in each of the following, using the prime factorization method:
144, 252, 630

Find the HCF of the numbers in each of the following, using the prime factorization method:
1197, 5320, 4389

Find the HCF of the numbers in each of the following, using the division method:
58, 70

Find the HCF of the numbers in each of the following, using the division method:
399, 437

Find the HCF of the numbers in each of the following, using the division method:
1045, 1520

Find the HCF of the numbers in each of the following, using the division method:
1965, 2096

Find the HCF of the numbers in each of the following, using the division method:
2241, 2324

Find the HCF of the numbers in each of the following, using the division method:
658, 940, 1128

Find the HCF of the numbers in each of the following, using the division method:
391, 425, 527

Find the HCF of the numbers in each of the following, using the division method:
1794, 2346, 4761

Show that the following pairs are co-primes:
59, 97

Show that the following pairs are co-primes:
161, 192

Show that the following pairs are co-primes:
343, 432

Show that the following pairs are co-primes:
512, 945

Show that the following pairs are co-primes:
385, 621

Show that the following pair is co-prime.

847, 1014

Find the greatest number which divides 615 and 963, leaving the remainder 6 in each case.

Find the greatest number which divides 2011 and 2623, leaving remainders 9 and 5 respectively.

Find the greatest number that will divide 445, 572 and 699, leaving remainders 4, 5, 6 respectively.

Reduce each of the following fraction to the lowest term:
`161/207`

Reduce each of the following fraction to the lowest term:
`517/799`

Reduce each of the following fraction to the lowest term:
`296/481`

Three pieces of timber, 42-m, 49-m and 63-m long, have to be divided into planks of the same length. What is the greatest possible length of each plank?

Three different containers contain 403 L, 434 L and 465 L of milk respectively. Find the capacity of a container which can measure the milk of all the containers in an exact number of times.

There are 527 apples, 646 pears, and 748 oranges. These are to be arranged in heaps containing the same number of fruits. Find the greatest number of fruits possible in each heap. How many heaps are formed?

Determine the longest tape which can be used to measure exactly the lengths 7 m, 3 m 85 cm, and 12 m 95 cm.

A rectangular courtyard is 18 m 72 cm long and 13 m 20 cm broad. It is to be paved with square tiles of the same size. Find the least possible number of such tiles.

Find the HCF of
Two prime numbers

Find the HCF of
Two consecutive numbers

Find the HCF of
Two co-primes

Find the HCF of
2 and an even number

Find the LCM of the numbers given below:
42, 63

Find the LCM of the numbers given below:
60, 75

Find the LCM of the numbers given below:
12, 18, 20

Find the LCM of the numbers given below:
36, 60, 72

Find the LCM of the numbers given below:
36, 40, 126

Find the LCM of the numbers given below:
16, 28, 40, 77

Find the LCM of the numbers given below:
28, 36, 45, 60

Find the LCM of the numbers given below:
144, 180, 384

Find the LCM of the numbers given below:
48, 64, 72, 96, 108

Find the HCF and LCM of:
117, 221

Find the HCF and LCM of:
234, 572

Find the HCF and LCM of
693, 1078

Find the HCF and LCM of
145, 232

Find the HCF and LCM of
861, 1353

Find the HCF and LCM of
2923, 3239

For the below pair of numbers, verify that their product = (HCF × LCM).
87, 145

For the below pair of numbers, verify that their product = (HCF × LCM).
186, 403

For the below pair of numbers, verify that their product = (HCF × LCM).
490, 1155

The product of two numbers is 2160 and their HCF is 12. Find their LCM.

The product of two numbers is 2160 and their LCM is 320. Find their HCF.

The HCF of two numbers is 145 and their LCM is 2175. If one of the numbers is 725, find the other.

The HCF and LCM of two numbers are 131 and 8253 respectively. If one of the numbers is 917, find the other.

Find the least number divisible by 15, 20, 24, 32, and 36.

Find the least number which when divided by 25, 40, and 60 leaves 9 as the remainder in each case.

Find the least number of five digits that is exactly divisible by 16, 18, 24 and 30.

Find the greatest number of five digits exactly divisible by 9, 12, 15, 18 and 24.

Three bells toll at intervals of 9, 12, 15 minutes. If they start tolling together, after what time will they next toll together?

Three boys step off together from the same place. If their steps measure 36 cm, 48 cm and 54 cm, at what distance from the starting point will they again step together?

The traffic lights at three different road crossings change after every 48 seconds, 72 seconds, and 108 seconds respectively. If they change simultaneously at 7 a.m., at what time will they change simultaneously again?

Which of the following numbers is divisible by 3?

Which of the following numbers is divisible by 9?

Which of the following numbers is divisible by 4?

Which of the following numbers is divisible by 8?

Which of the following numbers is divisible by 6?
(a) 8790432
(b) 98671402
(c) 85492014
(d) none of these

Which of the following numbers is divisible by 11?

Which of the following is a prime number?

Which of the following is a prime number?

Which of the following is a prime number?

Which of the following are co-primes?

Which of the following is a composite number?

The HCF of 144 and 198 is

The HCF of 144 and 198 is

Which of the following are co-primes?

The greatest number which divides 134 and 167 leaving 2 as remainder in each case is

The LCM of 24, 36, 40 is

The LCM of 12, 15, 20, 27 is

The smallest number which when diminished by 3 is divisible by 14, 28, 36 and 45, is

The HCF of two co-primes is

If a and b are co-primes, then their LCM is

The product of two numbers is 2160 and their HCF is 12. The LCM of these numbers is

The HCF of two numbers is 145 and their LCM is 2175. If one of the numbers is 725, the other number is

The least number divisible by each of the numbers 15, 20, 24, 32 and 36 is

Three bells toll together at intervals of 9, 12, 15 minutes. If they start tolling together, after what time will they next toll together?

Which of the following are co-primes?

The LCM of two co-prime numbers is their

What least number should be replaced for * so that the number 67301*2 is exactly divisible by 9?

Which of the following numbers is divisible by 6?

Which of the following is a prime number?

Every counting number has an infinite number of

1 is neither ______ nor ______.

The smallest prime number is ______.

The smallest composite number is ______.

Fill in the blank.

The HCF of two consecutive odd numbers is _________

Fill in the blank.

Two perfect numbers are ________ and _______

Write 'T' for true and 'F' for false for the following statement.

Every prime number is odd.

Write 'T' for true and 'F' for false for the following statement.

Every even number is composite.

Write 'T' for true and 'F' for false for the following statement.

The sum of two odd numbers is always odd.

Write 'T' for true and 'F' for false for the following statement.

The sum of two even numbers is always even.

Write 'T' for true and 'F' for false for the following statement.

The HCF of two given numbers is always a factor is their LCM.