Question

Find the largest number which divides 2053 and 967 leaving remainderas 5 and 7 ???

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