Question

Find the largest number that will divide 2053 and 967 and leaves a remainder of 5 and 7 respectively.

Answer 1

it is given that on dividing 2053 by the required number there is a remainder of 5 .this mean that 2053 - 5 = 2048 is exactly divisible by required number . similarly,
967 - 7 = 960
the required number is the largest number satisfying the above property .
therefore ,it is the HCF of 2048 & 960
HCF of 2048 & 960 is 64 
hence required number is 64

Answer 2

GIVEN; 2053 leaves reminder 5

so, 2053 - 5 = 2048

AND; 967 LEAVES REMINDER 7.

so; 967 - 7 = 960

NOW, IT HCF ( as we need to find largest no.)

HCF =

2048= 2^11 AND 960= 2^6*3* 5.

HCF =2^6 ; =64

HOPE IT HELPS!!!