Question

What is the GCF between 120, 144?

Answer 1

`GCF(144,120)=24.`

Explanation:

The GCF is the largest integer that divides exactly into both numbers.

For larger numbers the GCF can be found using the Euclidean algorithm, instead of listing all the factors. (Of course it works for smaller numbers as well!)

Euclidean algorithm is.

`a=pb+r,`

`a,p,b , r inZZ`

`GCF(144,120)`

Express the larger one in terms of the smaller one.

`144=120xx1+24`

express the smaller one in terms of the reminder and continue until

`r=0`

`120=24xx1+0`

when the remainder is zero the GCF is the last non zero remainder

`GCF(144,120)=24.`