Find the Greatest Number Which Divides 285 and 1249 Leaving Remainders 9 and 7

Video Explanation

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

Solution

Question: Find the greatest number which divides 285 and 1249 leaving remainders 9 and 7 respectively.

Step 1: Subtract the Given Remainders

If a number leaves remainder 9 when dividing 285, then it exactly divides:

285 − 9 = 276

If a number leaves remainder 7 when dividing 1249, then it exactly divides:

1249 − 7 = 1242

Step 2: Find the HCF of 276 and 1242

Using Euclid’s division algorithm:

1242 = 276 × 4 + 138

276 = 138 × 2 + 0

Since the remainder is zero,

∴ HCF (276, 1242) = 138

Final Answer

∴ The greatest number which divides 285 and 1249 leaving remainders 9 and 7 respectively is 138.

Conclusion

Thus, by subtracting the given remainders and applying Euclid’s division algorithm, we find that the required greatest number is 138.