Question

Find the greatest possible length of each piece that can be lacing without being wasted ifYou want to make woven plastic bracelets. You have 3 pieces of plastic lacing with lengths 45cm,75cm, and60cm. You need to cut the lacing into pieces of the same length.

Short answer

The greatest possible length that can be use is $15cm$.

Step-by-step solution

Step -1 - Apply the concept of   GCF.

In this, simply use the concept of finding the GCF by doing the factors of the number and find the factor which is common and greatest from them.

Step -2 – Find the common factors

Here, the two lengths are 45,75,60.

The factor of 45 is 45=1,3,5,9,15,45

The factor of 75 is 75=1,3,5,15,25,75

The factor of 60 is 60=1,2,3,4,5,6,10,12,15,20,30,60

Step -3 – Finding the GCF 

Now, the common factor among both the number is 15.

So, the greatest common factor is15 .

Therefore, without wasting the greatest possible length of each piece should be 15cm.