Advertisements
Advertisements
Question
Explain why 7 × 11 × 13 + 13 and 7 × 6 × 5 × 4 × 3 × 2 × 1 + 5 are composite numbers.
Solution
Numbers are of two types - prime and composite. Prime numbers can be divided by 1 and only itself, whereas composite numbers have factors other than 1 and itself.
It can be observed that,
7 × 11 × 13 + 13
= 13 (7 × 11 + 1)
= 13 × (77 + 1)
= 13 × 78
= 3 × 13 × 6
The given expression has 6 and 13 as its factors. Therefore, it is a composite number.
7 × 6 × 5 × 4 × 3 × 2 × 1 + 5
= 5 × (7 × 6 × 4 × 3 × 2 × 1 + 1)
= 5 × (1008 + 1)
= 5 × 1009
1009 cannot be factorized further. Therefore, the given expression has 5 and 1009 as its factors. Hence, it is a composite number.
APPEARS IN
RELATED QUESTIONS
Consider the number 12n where n is a natural number. Check whether there is any value of n ∈ N for which 12n ends with the digital zero.
Express the number as a product of its prime factor:
140
State fundamental theorem of arithmetic?
Determine the prime factorisation of each of the following positive integer:
20570
Determine the prime factorisation of each of the following positive integer:
58500
Express the number as a product of its prime factor:
5005
If m, n are natural numbers, for what values of m, does 2n × 5m ends in 5?
If p1x1 × p2x2 × p3x3 × p4x4 = 113400 where p1, p2, p3, p4 are primes in ascending order and x1, x2, x3, x4, are integers, find the value of p1, p2, p3, p4 and x1, x2, x3, x4
The sum of the exponents of the prime factors in the prime factorization of 1729 is
There is a circular path around a sports field. Priya takes 18 minutes to drive one round of the field. Harish takes 12 minutes. Suppose they both start at the same point and at the same time and go in the same direction. After how many minutes will they meet?
The largest number which divides 60 and 75, leaving remainders 8 and 10 respectively, is ______.
According to the fundamental theorem of arithmetic, if T (a prime number) divides b2, b > 0, then ______.
n2 – 1 is divisible by 8, if n is ______.
The least number that is divisible by all the numbers from 1 to 10 (both inclusive) is ______.
On a morning walk, three persons step off together and their steps measure 40 cm, 42 cm and 45 cm, respectively. What is the minimum distance each should walk so that each can cover the same distance in complete steps?
Statement A (Assertion): If product of two numbers is 5780 and their HCF is 17, then their LCM is 340.
Statement R (Reason): HCF is always a factor of LCM.
Show the 6n cannot end with digit 0 for any natural number 'n'.
Assertion (A): The HCF of two numbers is 5 and their product is 150. Then their LCM is 40.
Reason(R): For any two positive integers a and b, HCF (a, b) × LCM (a, b) = a × b.
If n is a natural number, then 8n cannot end with digit
National Art convention got registrations from students from all parts of the country, of which 60 are interested in music, 84 are interested in dance and 108 students are interested in handicrafts. For optimum cultural exchange, organisers wish to keep them in minimum number of groups such that each group consists of students interested in the same artform and the number of students in each group is the same. Find the number of students in each group. Find the number of groups in each art form. How many rooms are required if each group will be allotted a room?
