Question

Using Euclid’s division algorithm, find the largest number that divides 1251, 9377 and 15628 leaving remainders 1, 2 and 3, respectively.

Answer 1

Solution:
Since, 1, 2 and 3 are the remainders of 1251, 9377 and 15628 respectively.
So, 1251 – 1 = 1250 is exactly divisible by the required number,
9377 – 2 = 9375 is exactly divisible by the required number,
15628 – 3 = 15625 is exactly divisible by the required number.
So, required number = HCF of 1250, 9375 and 15625.
By Euclid’s division algorithm,
15625 = 9375 x 1 + 6250
9375 = 6250 x 1 + 3125
6250 = 3125 x 2 + 0
=> HCF (15625, 9375) = 3125
3125 = 1250 x 2 + 625
1250 = 625 x 2 + 0

HCF(3125, 1250) = 625
So, HCF (1250, 9375, 15625) = 625
Hence, the largest number is 625.