Question

Find the largest number which divides 320 and 457, leaving remainders 5 and 7 respectively.

Answer 1

To find the largest number which when divides 320 and 457 leaving the remainders 5 and 7 respectively. First we subtract the remainders from the given numbers and then calculate the HCF of New numbers.
Given numbers are 320 & 457 and remainders are 5 & 7.Then new numbers after Subtracting remainders are :(320 - 5) = 315 and (457- 7)= 450
We have to find the HCF of 315 and 450 by using Euclid's division Lemma, a= bq+r
Here, 450>315
450 = 315 x 1 + 135
315 = 135 x 2 + 45
135 = 45 x 3 + 0
Therefore HCF of 450 & 315 is 45.
Hence, the largest number which divides 320 and 457 leaving remainders 5 and 7 respectively is 45.