Find the Largest Number Which Divides 626, 3127 and 15628 Leaving Remainders 1, 2 and 3

Video Explanation

Watch the video below to understand the complete solution step by step:

Solution

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

Step 1: Subtract the Given Remainders

If a number leaves remainder 1 when dividing 626, then it exactly divides:

626 − 1 = 625

If a number leaves remainder 2 when dividing 3127, then it exactly divides:

3127 − 2 = 3125

If a number leaves remainder 3 when dividing 15628, then it exactly divides:

15628 − 3 = 15625

Step 2: Find the HCF of 625, 3125 and 15625

Using Euclid’s division algorithm:

3125 = 625 × 5 + 0

15625 = 625 × 25 + 0

Since the remainder is zero in both cases,

∴ HCF (625, 3125, 15625) = 625

Final Answer

∴ The largest number that divides 626, 3127 and 15628 leaving remainders 1, 2 and 3 respectively is 625.

Conclusion

Thus, by subtracting the given remainders and applying Euclid’s division algorithm, we find that the required largest number is 625.