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

Explanation

To find the largest number that divides 1251, 9377, and 15628 leaving remainders 1, 2, and 3 respectively, we can use Euclid's division algorithm. Here’s how to solve the problem step by step:

### Step 1: Adjust the numbers to remove the remainders
We need to subtract the remainders from each of the numbers:
- For 1251 with a remainder of 1:
\[ 1251 - 1 = 1250 \]
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