Question

Use euclid's division algorithm , find the largest number that divides 1251,9377 and 15628 leaving remainders 1,2 and 3.

Answer 1

=>> Given numbers = 1251, 9377, 15628
Given remainders = 1, 2, 3
So, The largest number that divides 1251, 9377, 15628 leaving remainders 1, 2 and 3 respectively = HCF [(1251-1=1250), (9377-2=9375) and (15628-3=15625)]
We have,
9375 > 1250
By EDL,
9375 = 1250 x 7 + 625
1250=625x2+0
So HCF (9375,1250)= 625
Now HCF of 625, 15625
We have, 15625 > 625
By EDL,
15625 = 625 x 25 +0
So HCF (1250, 9375, 15625)= 625
Hope it helps