Question

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

Answer 1

The required number when divides 445, 572 and 699 leaves remainders 4, 5 and 6

This means 445 – 4 = 441, 572 – 5 = 561 and 699 – 6 = 693 are completely divisible by the number

∴ The required number = HCF of 441, 567 and 693

First consider 441 and 567

By applying Euclid’s division lemma

567 = 441 × 1 + 126

441 = 126 × 3 + 63

126 = 63 × 2 + 0

∴ HCF of 441 and 567 = 63

Now consider 63 and 693

By applying Euclid’s division lemma

693 = 63 × 11 + 0

∴ HCF of 441, 567 and 693 = 63

Hence required number is 63.