Question

three strings are of lengths 120 cm, 136 cm and 160 cm. if these strings areto be cut into smaller pieces of equal length, what is the length of the longest string possible?

Answer 1

Answer :

Given : Three strings are of lengths 120 cm, 136 cm and 160 cm.

Now we want to cut smaller pieces with equal length . So to find longest string possible we find H.C.F. of all these lengths , As :

120 = 2 $\times$ 2 $\times$ 2 $\times$ 3 $\times$ 5

And

136 = 2 $\times$ 2 $\times$ 2 $\times$ 17

And
160 = 2 $\times$ 2 $\times$ 2 $\times$ 2 $\times$ 2 $\times$ 5

So,

H.C.F. ( 120 , 136 , 160 ) = 2 $\times$ 2 $\times$ 2 = 8

SO,

we can cut longest string of 8 cm ( Ans )