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    GCF for 24, 36 and 60

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

    What's the Greatest Common Factor (GCF) of 24, 36 and 60?

    Answer

    GCF of 24, 36 and 60 is
    12

    (Twelve)

    12 is the largest positive integer that divides 24, 36 and 60 without a remainder — every other common divisor of the three divides it too.

    Finding the GCF of 24, 36 and 60 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 24: 2 × 2 × 2 × 3 (exponent form: 23 × 3)

    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)

    Prime factor243660Lowest power
    223222222
    333233
    5——5—

    GCF = 2 × 2 × 3 = 12

    Checking the GCF of 24, 36 and 60 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(24, 36) = 12

    GCF(12, 60) = 12

    GCF(24, 36, 60) = 12

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

    24 ÷ 12 = 2

    36 ÷ 12 = 3

    60 ÷ 12 = 5

    2, 3 and 5 have no common factor left — that is what makes 12 the greatest one.

    Related Calculations

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    What is the GCF of 24, 36 and 60?. The GCF of 24, 36 and 60 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
    2436453
    2436462
    2436471
    24364812
    2436491
    2436502
    2436513
    2436524
    2436531
    2436546
    2436551
    2436564
    2436573
    2436582
    2436591
    24366012
    2436611
    2436622
    2436633
    2436644
    2436651
    2436666
    2436671
    2436684
    2436693
    2436702
    2436711
    24367212
    2436731
    2436742

    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 24, 36 and 60? (The answer is: 12). Enter the first number (e.g. '24'), the second (e.g. '36') and the third (e.g. '60'), 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 24, 36 and 60?

    GCF of 24, 36 and 60 is 12

    What prime factors do 24, 36 and 60 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 24, 36 and 60 two numbers at a time?

    Yes, and it is the check this page prints. The GCF of 24 and 36 is 12, and the GCF of 12 and 60 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 24 : 36 : 60?

    Divide every term by the GCF 12: 24 ÷ 12 = 2, 36 ÷ 12 = 3 and 60 ÷ 12 = 5. So 24 : 36 : 60 in lowest terms is 2 : 3 : 5, and no whole number other than 1 divides all three of those.

    See Also