Question

What is the largest number that divides 626, 3127 and 15628 and leaves remainders of 1, 2 and 3 respectively.

Answer 1

SOLUTION :  

To find the greatest number which when divides 626, 3127 and 15628 leaving the remainders 1,2 and 3 respectively.First ,we subtract the remainder from the given numbers and then calculate the HCF of new numbers.

Given numbers are  626, 3127 and 15628 and  remainders are 1,2 and 3

Then ,new numbers after subtracting remainders are :

626 – 1 = 625, 3127 – 2 = 3125, 15628 – 3 = 15625  

Now, we have to find the H.C.F. of 625, 3125 and 15625.

First we find the HCF of  625 and 3125.

By applying Euclid’s division lemma,a = bq+r

Let a = 3125  and b = 625

3125 = 625 x 5 + 0.

Here remainder is zero , and the last divisor is 625.

So H.C.F. of 625 and 3125 is 625.

Now,we find the HCF of 625 and 15625.

By applying Euclid’s division lemma,a = bq+r

Let a = 15626 and b = 625

15625 = 625 x 25 + 0

Here remainder is zero , and the last divisor is 625.

So H.C.F. of 625 and 3125 is 625.

Therefore,H.C.F. of 625, 3125 and 15625 is 625

Hence, the required greatest number is 625

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