Question

What is the greatest common factor of `16 and 30`?

Answer 1

See a solution process below:

Explanation:

First, factor each of the numbers as:

`16 = 2 xx 2 xx 2 xx 2`

`30 = 2 xx 3 xx 5`

Next, identify the common factors for each number:

`16 = color(red)(2) xx 2 xx 2 xx 2`

`30 = color(red)(2) xx 3 xx 5`

Therefore the Greatest Common Factor is:

`"GCF" = color(red)(2)`

Answer 2

2

Explanation:

Use trial and error to go through each possible factor:

2: `16/2 = 8` and `30/2 = 15` so 2 is a factor. Let's keep going up

3: Can't divide 16 by 3 to get a whole number so 3 is not a common factor even if it is for 30

4: Can't divide 30 by 4 to get a whole number so 4 is not a common factor

5: Can't divide 16 by 5 to get a whole number so 5 is not a common factor

These are the main numbers you test if the answer doesn't seem obvious. As 2 was the largest factor we got, it's the answer.