Question

Sam has 3 pieces of ropes length 150 cm, 140 cm, and 210 cm. He wishes to cut these ropes into smaller pieces of equal length with no remainder.What is the greatest possible length of each of the smaller pieces?

Answer 1

150=3×5×5×2
140=2×7×2×5
210=3×7×2×5
so,the greatest possible length of each=10

Answer 2

Solution :-

To find the smaller pieces of ropes of equal length with no remainder, we will have to calculate the HCF of 150, 140 and 210

HCF of 150, 140 and 210

Prime Factors of 150 = 2*3*5*5*

Prime Factors of 140 = 2*2*5*7

Prime Factors of 210 = 2*3*5*7

Common Factors among these = 2*5 = 10

So, HCF of 150, 140 and 210 is 10

Sam will have to cut these ropes into pieces of equal length of 10 cm so that there will be no remainder.

Answer