Question

The largest number which divides 60 and 75, leaving remainders 8 and 10 respectively is

Answer 1

Answer:

52 and 60 are the correct answers

Answer 2

Given: Two numbers-  60 and 75

To find: The largest number which divides 60 and 75 leaving remainder 8 and 10 respectively

Solution: Given that we need to find the largest number which when divides 60, leaves remainder 8 and when divides 75, leaves remainder 10.

The required number is the HCF of numbers obtained after deducting remainders from the given numbers.

i.e. 60 - 8 = 52 and 75 - 10 = 65

We need to calculate the LCM of 52 and 65.

Using Prime factorization method:

52 = 2 × 2 × 13 × 1

65 = 5 × 13 × 1

HCF is the product of common factors of given numbers.

HCF = 13 × 1 (13 and 1 are the common factors of 52 and 65) = 13

On dividing 60 and 75 by 13, we can observe that the remainders are 8 and 10 respectively.

Hence, the largest number which divides 60 and 75 leaving remainder 8 and 10 respectively is 13.