Question

find the largest number that divides 2053 and 967 and leaves a remainder of 5 and 7 tespectively

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

first we will subtract 2053 and 967 by 5 and 7 respectively
2053-5= 2048
967-7= 960


largest number means we have to find its HCF
2048 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2


Find the prime factorization of 960
960 = 2 × 2 × 2 × 2 × 2 × 2 × 3 × 5

Multiply all the common factors obtained in steps i) and ii) above to find the HCF:

HCF = 2 × 2 × 2 × 2 × 2 × 2
HCF = 64