Question

Two ropes, one 8 meters long and the other 12 meters long are to be cut into pieces of the same length. What will the maximum possible length of each piece be?

Answer 1

Length of one rope = 8 m

Length of other rope = 12 m

The maximum possible length of each piece of rope of the same length that can be cut from the two given ropes is the HCF of 8 m and 12 m.

Factors of 8: 1, 2, 4, 8

Factors of 12: 1, 2, 3, 4, 6, 12

Common factors of 8 and 12: 1, 2, 4

HCF of 8 and 12 = 4

∴ Maximum possible length of each piece of rope of same length = 4 m

Thus, the maximum possible length of each piece of rope is 4 m.