Question

A trader has three bundles of rope 392 m, 308 m and 490 m long. What is the greatest length of rope that the bundles can be cut up into without any left over rope?

• A. 7 m
• B. 14 m
• C. 10 m
• D. 25 m

Answer 1

The correct option is B 14 m

To find the greatest length of rope that the bundles can be cut up into without any left over rope, we need to find their H.C.F

Factors of 392 $=2\times 2\times 2\times 7\times 7$
Factors of 308 $=2\times 2\times 7\times 11$
Factors of 490 $=2\times 5\times 7\times 7$

H.C.F of 392, 308 and 490 $=2\times 7=14$
Hence, the greatest length of rope that the bundles can be cut up into without any left over rope = 14 m