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    GCF for 40, 60 and 100

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

    What's the Greatest Common Factor (GCF) of 40, 60 and 100?

    Answer

    GCF of 40, 60 and 100 is
    20

    (Twenty)

    20 is the largest positive integer that divides 40, 60 and 100 without a remainder — every other common divisor of the three divides it too.

    Finding the GCF of 40, 60 and 100 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 40: 2 × 2 × 2 × 5 (exponent form: 23 × 5)

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

    All Prime Factors of 100: 2 × 2 × 5 × 5 (exponent form: 22 × 52)

    Prime factor4060100Lowest power
    223222222
    3—3——
    555525

    GCF = 2 × 2 × 5 = 20

    Checking the GCF of 40, 60 and 100 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(40, 60) = 20

    GCF(20, 100) = 20

    GCF(40, 60, 100) = 20

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

    40 ÷ 20 = 2

    60 ÷ 20 = 3

    100 ÷ 20 = 5

    2, 3 and 5 have no common factor left — that is what makes 20 the greatest one.

    Related Calculations

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    What is the GCF of 40, 60 and 100?. The GCF of 40, 60 and 100 is 20 — 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
    4060855
    4060862
    4060871
    4060884
    4060891
    40609010
    4060911
    4060924
    4060931
    4060942
    4060955
    4060964
    4060971
    4060982
    4060991
    406010020
    40601011
    40601022
    40601031
    40601044
    40601055
    40601062
    40601071
    40601084
    40601091
    406011010
    40601111
    40601124
    40601131
    40601142

    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 40, 60 and 100? (The answer is: 20). Enter the first number (e.g. '40'), the second (e.g. '60') and the third (e.g. '100'), 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 40, 60 and 100?

    GCF of 40, 60 and 100 is 20

    What prime factors do 40, 60 and 100 share?

    All three factorizations contain 2 × 2 × 5, and multiplying those shared primes gives 20 — exactly the greatest common factor.

    Can you get the GCF of 40, 60 and 100 two numbers at a time?

    Yes, and it is the check this page prints. The GCF of 40 and 60 is 20, and the GCF of 20 and 100 is 20 — 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 40 : 60 : 100?

    Divide every term by the GCF 20: 40 ÷ 20 = 2, 60 ÷ 20 = 3 and 100 ÷ 20 = 5. So 40 : 60 : 100 in lowest terms is 2 : 3 : 5, and no whole number other than 1 divides all three of those.

    See Also