Question

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

Answer 1

Subtract 1, 2, 3 from 1251, 9377, 15628 respectively. 

1251 - 1 = 1250, 

9377 - 2 = 9375, 

15628 - 3 = 15625 

Find the HCF of 1250 and 9375 

9375 = 1250 x 7 + 625

1250 = 625 x 2 + 0 

thus 625 is the HCF 

Now, find the HCF of 625 and 15625 

15625 = 625 x 25 + 0 

Thus 625 is the number that divides 1251, 9377 and 15628 leaving the remainders 1, 2 and 3 respective.