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?

5 Answers

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  • 2 months ago

    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.

  • sepia
    Lv 7
    2 months ago

    216 = 2^3 × 3^3

    216 is the greatest common divisor of 216

    gcd(216)

  • 2 months ago

    18 is greatest common factor of 216?

  • 2 months ago

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

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  • Jim
    Lv 7
    2 months ago

    Greatest Common Factor only applies when comparing 2 different numbers.

    Attachment image
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