Find the Greatest Number Which Divides 2011 and 2623 Leaving Remainders 9 and 5

Video Explanation

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

Solution

Question: Find the greatest number which divides 2011 and 2623 leaving remainders 9 and 5 respectively.

Step 1: Subtract the Given Remainders

If a number leaves remainder 9 when dividing 2011, then it exactly divides:

2011 − 9 = 2002

If a number leaves remainder 5 when dividing 2623, then it exactly divides:

2623 − 5 = 2618

Step 2: Find the HCF of 2002 and 2618

Using Euclid’s division algorithm:

2618 = 2002 × 1 + 616

2002 = 616 × 3 + 154

616 = 154 × 4 + 0

Since the remainder is zero,

∴ HCF (2002, 2618) = 154

Final Answer

∴ The greatest number which divides 2011 and 2623 leaving remainders 9 and 5 respectively is 154.

Conclusion

Thus, by subtracting the given remainders and applying Euclid’s division algorithm, we find that the required greatest number is 154.