Question

Find the largest number which on dividing 1251, 9377 and 15628 leaves remainders 1, 2 and 3 respectively.

Answer 1

On subtracting 1, 2 and 3 from 1251, 9377 and 15628 respectively, we get 1250, 9375 and 15625.

Now, we find the HCF of 1250 and 9375 by using Euclid's division lemma

9375 = 1250 × 7 + 625

∵ Remainder is not zero,
∴ we divide 1250 by 625 by using Euclid's division lemma

1250 = 625 × 2 + 0

Since, remainder is zero,
Therefore, HCF of 1250 and 9375 is 625.

Now, we find the HCF of 15625 and 625 by using Euclid's division lemma

15625 = 625 × 25 + 0

Since, remainder is zero,
Therefore, HCF of 15625 and 625 is 625.

Thus, HCF of 1250, 9375 and 15625 is 625.

Hence, the largest number which on dividing 1251, 9377 and 15628 leaves remainders 1, 2 and 3 respectively is 625.