Tom has three pieces of rope with lengths of 140 cm, 168 cm and 210 cm. He wishes to cut the three pieces of rope into smaller pieces of equal length with no remainders.

Question

a) what is the greatest possible length of each of the smaller pieces of rope?

b) how many of the smaller pieces of rope of equal lenght can he get?

Answer 1

140 = 2^2 * 5 * 7
168 = 2^3 * 3 * 7
210 = 2 * 3 * 5 * 7

So, what is the biggest number that divides all of those?

Answer 2

14