Find the greatest number by which on dividing 2056 and 967 the remainder are obtained as 5 and 7 respectively.

It is mentioned in the question that that on dividing 2053 by the required number there is a remainder of 5 which means that 2053 - 5 = 2048 is exactly divisible by required number . In the similar manner,

967 - 7 = 960 the required number is the largest number satisfying the above property.

Therefore, it is the HCF of 2048 & 960

2048 = 64 × 32

= 2⁶ × 2⁵

= 2¹¹

960 = 5 × 2 × 2 × 2 × 2 × 2 × 2 × 3

So for finding the HCF we may write as follows:

Common Factor Least Power

2 6

So HCF = 2⁶

= 64

HCF of 2048 & 960 is 64

Hence required number is 64