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    GCF for 12, 24 and 36

    "Greatest Common Factor of 3 Numbers" Calculator
    Greatest Common Factor of
    ,
    and

    What's the Greatest Common Factor (GCF) of 12, 24 and 36?

    Answer

    GCF of 12, 24 and 36 is
    12

    (Twelve)

    12 is the largest positive integer that divides 12, 24 and 36 without a remainder — every other common divisor of the three divides it too.

    Finding the GCF of 12, 24 and 36 by Prime Factorization

    Split all three numbers into prime factors, then keep every prime that appears in all three of them, each taken as many times as it appears in the poorest factorization. Multiplying what is left gives the greatest common factor:

    All Prime Factors of 12: 2 × 2 × 3 (exponent form: 22 × 3)

    All Prime Factors of 24: 2 × 2 × 2 × 3 (exponent form: 23 × 3)

    All Prime Factors of 36: 2 × 2 × 3 × 3 (exponent form: 22 × 32)

    Prime factor122436Lowest power
    222232222
    333323

    GCF = 2 × 2 × 3 = 12

    Checking the GCF of 12, 24 and 36 Two Numbers at a Time

    The greatest common factor is associative, so three numbers can be handled as two pairs — and this is what makes the Euclidean algorithm usable here: run it on the first pair, then run it again on that result and the third number.

    GCF(a, b, c) = GCF(GCF(a, b), c)

    GCF(12, 24) = 12

    GCF(12, 36) = 12

    GCF(12, 24, 36) = 12

    The answer checks out by division — all three quotients come out whole:

    12 ÷ 12 = 1

    24 ÷ 12 = 2

    36 ÷ 12 = 3

    1, 2 and 3 have no common factor left — that is what makes 12 the greatest one.

    Related Calculations

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    What is the GCF of 12, 24 and 36?. The GCF of 12, 24 and 36 is 12 — the largest number that divides all three with no remainder. Step-by-step solution for three numbers.
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    GCF Table

    Number 1Number 2Number 3GCF
    1221243
    1222242
    1223241
    12242412
    1224251
    1224262
    1224273
    1224284
    1224291
    1224306
    1224311
    1224324
    1224333
    1224342
    1224351
    12243612
    1224371
    1224382
    1224393
    1224404
    1224411
    1224426
    1224431
    1224444
    1224453
    1224462
    1224471
    12244812
    1224491
    1224502

    About "Greatest Common Factor of 3 Numbers" Calculator

    This calculator finds the Greatest Common Factor (GCF) of three numbers at once, without doing it in two passes. For example, it can help you find out what's the Greatest Common Factor (GCF) of 12, 24 and 36? (The answer is: 12). Enter the first number (e.g. '12'), the second (e.g. '24') and the third (e.g. '36'), then hit the 'Calculate' button.
    The Greatest Common Factor of three numbers — also called the greatest common divisor (GCD) or highest common factor (HCF) — is the largest positive integer that divides all three of them with zero remainder
    "Greatest Common Factor of 3 Numbers" Calculator
    Greatest Common Factor of
    ,
    and

    FAQ

    What's the Greatest Common Factor (GCF) of 12, 24 and 36?

    GCF of 12, 24 and 36 is 12

    What prime factors do 12, 24 and 36 share?

    All three factorizations contain 2 × 2 × 3, and multiplying those shared primes gives 12 — exactly the greatest common factor.

    Can you get the GCF of 12, 24 and 36 two numbers at a time?

    Yes, and it is the check this page prints. The GCF of 12 and 24 is 12, and the GCF of 12 and 36 is 12 — the same answer, because the greatest common factor is associative and does not depend on the order of the three numbers.

    How does the GCF simplify the ratio 12 : 24 : 36?

    Divide every term by the GCF 12: 12 ÷ 12 = 1, 24 ÷ 12 = 2 and 36 ÷ 12 = 3. So 12 : 24 : 36 in lowest terms is 1 : 2 : 3, and no whole number other than 1 divides all three of those.

    See Also