Question

What is the greatest common factor of 4 and 10?

Answer 1

The greatest common factor is 2.

Explanation:

First, you can list all the factors of 4.
`1, 2, 4`

Next, list all the factors of 10:
`1, 2, 5, 10`

Now, look back at the two lists and see if any of the numbers are the same in both lists. If there is more than one, the greatest number will be the greatest common factor. In this case, the only common number is 2, and so it is automatically the greatest common factor.

Answer 2

The GCF = 2.

Both 4 and 10 are even, so they must have a common factor of 2.
In this case this is the only common factor (apart from 1).

Explanation:

A good approach for any question involving factors, GCF, LCM and roots is to write each number as the product of its prime factors .

If you have a number written as the product of its prime factors, then you know everything about that number!

`color(white)(xx.xxx)4 = color(red)(2) xx 2`
`color(white)(xxxxx)10 = color(red)(2) color(white)(xxx)xx5`

`color(white)(xxx)GCF = 2` We can see that 2 is common to both.

This is also a good way of finding the LCM, especially of big numbers.

`LCM = 2xx2xx5 =20`