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    GCF for 36, 60 and 84

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

    What's the Greatest Common Factor (GCF) of 36, 60 and 84?

    Answer

    GCF of 36, 60 and 84 is
    12

    (Twelve)

    12 is the largest positive integer that divides 36, 60 and 84 without a remainder — every other common divisor of the three divides it too.

    Finding the GCF of 36, 60 and 84 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 36: 2 × 2 × 3 × 3 (exponent form: 22 × 32)

    All Prime Factors of 60: 2 × 2 × 3 × 5 (exponent form: 22 × 3 × 5)

    All Prime Factors of 84: 2 × 2 × 3 × 7 (exponent form: 22 × 3 × 7)

    Prime factor366084Lowest power
    222222222
    332333
    5—5——
    7——7—

    GCF = 2 × 2 × 3 = 12

    Checking the GCF of 36, 60 and 84 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(36, 60) = 12

    GCF(12, 84) = 12

    GCF(36, 60, 84) = 12

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

    36 ÷ 12 = 3

    60 ÷ 12 = 5

    84 ÷ 12 = 7

    3, 5 and 7 have no common factor left — that is what makes 12 the greatest one.

    Related Calculations

    See Also

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    What is the GCF of 36, 60 and 84?. The GCF of 36, 60 and 84 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
    3660693
    3660702
    3660711
    36607212
    3660731
    3660742
    3660753
    3660764
    3660771
    3660786
    3660791
    3660804
    3660813
    3660822
    3660831
    36608412
    3660851
    3660862
    3660873
    3660884
    3660891
    3660906
    3660911
    3660924
    3660933
    3660942
    3660951
    36609612
    3660971
    3660982

    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 36, 60 and 84? (The answer is: 12). Enter the first number (e.g. '36'), the second (e.g. '60') and the third (e.g. '84'), 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 36, 60 and 84?

    GCF of 36, 60 and 84 is 12

    What prime factors do 36, 60 and 84 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 36, 60 and 84 two numbers at a time?

    Yes, and it is the check this page prints. The GCF of 36 and 60 is 12, and the GCF of 12 and 84 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 36 : 60 : 84?

    Divide every term by the GCF 12: 36 ÷ 12 = 3, 60 ÷ 12 = 5 and 84 ÷ 12 = 7. So 36 : 60 : 84 in lowest terms is 3 : 5 : 7, and no whole number other than 1 divides all three of those.

    See Also