Question

Tom has three pieces of rope of lengths 140 cm, 168 cm and 180 cm.
He cuts them into smaller pieces of equal length with no remainders.
What is the greatest possible length of each of the smaller pieces of rope?

Answer 1

We need the greatest common divisor of 140, 168 and 180.

gcd(140,168) = 28.
gcd(28,180): 180 = 28·6 + 12, 28 = 12·2 + 4, 12 = 4·3, so gcd = 4.

Thus the greatest possible length is 4 cm. (This yields 140/4 = 35, 168/4 = 42, 180/4 = 45 pieces.)