Question

find the greatest number that will divide 445,572 and 699,leaving remainder 4,5 and 6 respectively

Answer 1

Let N is the number in question.

We have : 445 = aN + 4 or 441 = aN

572 = bN + 5 or 567 = bN

699 = cN + 6 or 693 = cN

Since: 441 = 3² x 7²

567 = 3⁴ x 7

693 = 3² x 7 x 11

The common factors are: 3³ x 7 = 63 = N

Answer 2

The largest number that will divide 699, 572 and 445 leaving remainders 6, 5 and 4 respectively is the HCF of the numbers (699 – 6), (572 – 5) and (445 – 4) i.e. 693,567 and 441. HCF of 693, 567 and 441:
HCF of 693 and 567:
693 = 567 x 1 + 126.