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    GCF for 4, 8 and 12

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

    What's the Greatest Common Factor (GCF) of 4, 8 and 12?

    Answer

    GCF of 4, 8 and 12 is
    4

    (Four)

    4 is the largest positive integer that divides 4, 8 and 12 without a remainder — every other common divisor of the three divides it too.

    Finding the GCF of 4, 8 and 12 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 4: 2 × 2 (exponent form: 22)

    All Prime Factors of 8: 2 × 2 × 2 (exponent form: 23)

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

    Prime factor4812Lowest power
    222232222
    3——3—

    GCF = 2 × 2 = 4

    Checking the GCF of 4, 8 and 12 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(4, 8) = 4

    GCF(4, 12) = 4

    GCF(4, 8, 12) = 4

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

    4 ÷ 4 = 1

    8 ÷ 4 = 2

    12 ÷ 4 = 3

    1, 2 and 3 have no common factor left — that is what makes 4 the greatest one.

    Related Calculations

    See Also

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    What is the GCF of 4, 8 and 12?. The GCF of 4, 8 and 12 is 4 — 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
    1481
    2482
    3481
    4484
    4581
    4682
    4781
    4884
    4891
    48102
    48111
    48124
    48131
    48142
    48151
    48164
    48171
    48182
    48191
    48204
    48211
    48222
    48231
    48244
    48251
    48262
    48271
    48284
    48291
    48302

    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 4, 8 and 12? (The answer is: 4). Enter the first number (e.g. '4'), the second (e.g. '8') and the third (e.g. '12'), 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 4, 8 and 12?

    GCF of 4, 8 and 12 is 4

    What prime factors do 4, 8 and 12 share?

    All three factorizations contain 2 × 2, and multiplying those shared primes gives 4 — exactly the greatest common factor.

    Can you get the GCF of 4, 8 and 12 two numbers at a time?

    Yes, and it is the check this page prints. The GCF of 4 and 8 is 4, and the GCF of 4 and 12 is 4 — 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 4 : 8 : 12?

    Divide every term by the GCF 4: 4 ÷ 4 = 1, 8 ÷ 4 = 2 and 12 ÷ 4 = 3. So 4 : 8 : 12 in lowest terms is 1 : 2 : 3, and no whole number other than 1 divides all three of those.

    See Also