Question

Find the length of the longest rope that can be used to measure exactly the ropes of length 1m 20cm, 3m 60cm and 4m

Answer 1

To measure the length of the longest rope that can be used to measure exactly the ropes of length 1m 20cm, 3m 60cm and 4m we will find the H.C.F of 120 cm, 360 cm and 400 cm.

As you know , 1 meter = 100 cm

To find the HCF of 120,360 and 400 we will use prime factorization method.

120=2×2×2×3×5

360=2×2×2×3×3×5

400=2×2×2×2×5×5

H.C.F(120,360,400)=2×2×2×5=40

∵Length of the longest rope that can be used to measure exactly the ropes of length  120 cm, 360 cm and 400 cm= 40 cm