Find the Largest Number Which Exactly Divides 280 and 1245 Leaving Remainders 4 and 3

Video Explanation

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

Solution

Question: Find the largest number which exactly divides 280 and 1245 leaving remainders 4 and 3 respectively.

Step 1: Subtract the Given Remainders

If a number leaves remainder 4 when dividing 280, then it exactly divides:

280 − 4 = 276

If a number leaves remainder 3 when dividing 1245, then it exactly divides:

1245 − 3 = 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 largest number which exactly divides 280 and 1245 leaving remainders 4 and 3 respectively is 138.

Conclusion

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