Find the Largest Number Which Divides 615 and 963 Leaving Remainder 6

Video Explanation

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

Solution

Question: Find the largest number which divides 615 and 963 leaving remainder 6 in each case.

Step 1: Subtract the Remainder

If a number leaves remainder 6, then it exactly divides:

615 − 6 = 609

963 − 6 = 957

Step 2: Find the HCF of 609 and 957

Using Euclid’s division algorithm:

957 = 609 × 1 + 348

609 = 348 × 1 + 261

348 = 261 × 1 + 87

261 = 87 × 3 + 0

Since the remainder is zero,

∴ HCF (609, 957) = 87

Final Answer

∴ The largest number which divides 615 and 963 leaving remainder 6 in each case is 87.

Conclusion

Thus, by subtracting the remainder and applying Euclid’s division algorithm, we find that the required largest number is 87.