# Is 9 the greatest common factor of 216?

216 is a highly composite number.  The major factors all seem to be divisible by 9.

2 * 108

3 * 72

4 * 54

6 * 36

8 * 27

9 * 24

12 * 18

9, 18, 27, 36, 54, 72 and 108 are all divisible by 9.

Does this make 9 the greatest common factor of 216?

Relevance
• The word "common" implies that you are talking about 2 or more numbers that have a shared (common) factor.

You can't have a "common" factor of a single number.

The *greatest* single factor is the number itself -- 216

If you were talking about *two* (or more) numbers, then you would be talking about the greatest common factor.

Let's take 216 and 120

The factors of 216 are:

1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 108, 216

The factors of 120 are:

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120

The factors they have in common are:

1, 2, 3, 4, 6, 8, 12, 24

So the greatest common factor of those *two* numbers is 24.

GCF(216, 120) = 24

But it doesn't make any sense to talk about the greatest common factor of a single number.

• 216 = 2^3 × 3^3

216 is the greatest common divisor of 216

gcd(216)

• 18 is greatest common factor of 216?

• "greatest common factor" does not apply to one number only to two or more. 