# What is the largest number which divides 626, 3127 and 15628 and leaves remainders of 1, 2 and 3 respectively?

Given: 626, 3127 and 15628.

To find: Here we have to find the value of the greatest number which divides 626, 3127 and 15628 and leaves remainders of 1, 2 and 3 respectively.

Solution:

If the required number divide 626, 3127 and 15628 leaving remainders 1, 2 and 3 respectively, then this means that number will divide 625(626 $-$ 1), 3125(3127 $-$ 2) and 15625(15628 $-$ 3) completely.

Now, we just have to find the HCF of 625, 3125 and 15625.

First, let's find HCF of 625 and 3125 using Euclid's division algorithm:

Using Euclid’s lemma to get:
• $3125\ =\ 625\ \times\ 5\ +\ 0$

The remainder has become zero, and we cannot proceed any further.

Therefore the HCF of 625 and 3125 is the divisor at this stage, i.e., 625.

Now, let's find HCF of 625 and 15625 using Euclid's division algorithm:

Using Euclid’s lemma to get:
• $15625\ =\ 625\ \times\ 25\ +\ 0$

The remainder has become zero, and we cannot proceed any further.

Therefore the HCF of 625 and 15625 is the divisor at this stage, i.e., 625.

So, the greatest number which divides 626, 3127 and 15628 and leaves remainders of 1, 2 and 3 respectively is 625.

Updated on: 10-Oct-2022

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