Question

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

Answer 1

To find the greatest number that divides 445, 572 and 699 and leaves remainders of 4, 5 and 6 respectively. The required number when divides 445, 572 and 699 leaves remainders 4, 5 and 6 this means

445 – 4 = 441, 572 – 5 = 567 and 699 – 6 = 693 are completely divisible by the number.

Therefore, the required number = H.C.F. of 441, 567 and 693.

First consider 441 and 567.

By applying Euclid’s division lemma

567 = 441 x 1 + 126

441 = 126 x 3 + 63

126 = 63 x 2 + 0.

Therefore, H.C.F. of 441 and 567 = 63

Now, consider 63 and 693

By applying Euclid’s division lemma

693 = 63 x 11 + 0.

Therefore, H.C.F. of 441, 567 and 693 = 63

Hence, the required number is 63