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    GCF for 48, 64 and 96

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

    What's the Greatest Common Factor (GCF) of 48, 64 and 96?

    Answer

    GCF of 48, 64 and 96 is
    16

    (Sixteen)

    16 is the largest positive integer that divides 48, 64 and 96 without a remainder — every other common divisor of the three divides it too.

    Finding the GCF of 48, 64 and 96 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 48: 2 × 2 × 2 × 2 × 3 (exponent form: 24 × 3)

    All Prime Factors of 64: 2 × 2 × 2 × 2 × 2 × 2 (exponent form: 26)

    All Prime Factors of 96: 2 × 2 × 2 × 2 × 2 × 3 (exponent form: 25 × 3)

    Prime factor486496Lowest power
    224262524
    33—3—

    GCF = 2 × 2 × 2 × 2 = 16

    Checking the GCF of 48, 64 and 96 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(48, 64) = 16

    GCF(16, 96) = 16

    GCF(48, 64, 96) = 16

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

    48 ÷ 16 = 3

    64 ÷ 16 = 4

    96 ÷ 16 = 6

    3, 4 and 6 have no common factor left — that is what makes 16 the greatest one.

    Related Calculations

    See Also

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    What is the GCF of 48, 64 and 96?. The GCF of 48, 64 and 96 is 16 — 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
    4864811
    4864822
    4864831
    4864844
    4864851
    4864862
    4864871
    4864888
    4864891
    4864902
    4864911
    4864924
    4864931
    4864942
    4864951
    48649616
    4864971
    4864982
    4864991
    48641004
    48641011
    48641022
    48641031
    48641048
    48641051
    48641062
    48641071
    48641084
    48641091
    48641102

    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 48, 64 and 96? (The answer is: 16). Enter the first number (e.g. '48'), the second (e.g. '64') and the third (e.g. '96'), 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 48, 64 and 96?

    GCF of 48, 64 and 96 is 16

    What prime factors do 48, 64 and 96 share?

    All three factorizations contain 2 × 2 × 2 × 2, and multiplying those shared primes gives 16 — exactly the greatest common factor.

    Can you get the GCF of 48, 64 and 96 two numbers at a time?

    Yes, and it is the check this page prints. The GCF of 48 and 64 is 16, and the GCF of 16 and 96 is 16 — 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 48 : 64 : 96?

    Divide every term by the GCF 16: 48 ÷ 16 = 3, 64 ÷ 16 = 4 and 96 ÷ 16 = 6. So 48 : 64 : 96 in lowest terms is 3 : 4 : 6, and no whole number other than 1 divides all three of those.

    See Also