Find the Greatest Number Which Divides 445, 572 and 699 Leaving Remainders 4, 5 and 6

Video Explanation

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

Solution

Question: Find the greatest number that will divide 445, 572 and 699 leaving remainders 4, 5 and 6 respectively.

Step 1: Subtract the Given Remainders

If a number leaves remainder 4 when dividing 445, then it exactly divides:

445 − 4 = 441

If a number leaves remainder 5 when dividing 572, then it exactly divides:

572 − 5 = 567

If a number leaves remainder 6 when dividing 699, then it exactly divides:

699 − 6 = 693

Step 2: Find the HCF of 441, 567 and 693

Using Euclid’s division algorithm:

567 = 441 × 1 + 126

441 = 126 × 3 + 63

126 = 63 × 2 + 0

So, HCF (441, 567) = 63

Now find HCF of 63 and 693:

693 = 63 × 11 + 0

Since the remainder is zero,

∴ HCF (441, 567, 693) = 21

Final Answer

∴ The greatest number which divides 445, 572 and 699 leaving remainders 4, 5 and 6 respectively is 21.

Conclusion

Thus, by subtracting the given remainders and applying Euclid’s division algorithm, we find that the required greatest number is 21.