Advertisements
Advertisements
Question
The largest number which divides 70 and 125, leaving remainders 5 and 8, respectively, is ______.
Options
13
65
875
1750
Solution
The largest number which divides 70 and 125, leaving remainders 5 and 8, respectively, is 13.
Explanation:
We have to find the largest number which divides 70 and 125
Leaving remainders 5 and 8
This can be also written as,
To find the largest number which exactly divides (70 – 5) and (125 – 8)
The largest number that divides 65 and 117 is also the Highest Common Factor of 65 and 117
Therefore, the required number is the HCF of 65 and 117
Factors of 65 = 1, 5, 13, 65
Factors of 117 = 1, 3, 9, 13, 39, 117
Common Factors = 1, 13
Highest Common factor (HCF) = 13
i.e., The largest number which divides 70 and 125
Leaving remainders 5 and 8, respectively = 13
APPEARS IN
RELATED QUESTIONS
Find HCF and LCM of 404 and 96 and verify that HCF × LCM = Product of the two given numbers.
Write the sum of the exponents of prime factors in the prime factorization of 98.
If m, n are natural numbers, for what values of m, does 2n × 5m ends in 5?
When a number is divided by 7, its remainder is always ______.
For some integer m, every even integer is of the form ______.
For some integer q, every odd integer is of the form ______.
n2 – 1 is divisible by 8, if n is ______.
(HCF × LCM) for the numbers 70 and 40 is ______.
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?
The HCF of two numbers 65 and 104 is 13. If LCM of 65 and 104 is 40x, then the value of x is ______.
