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    GCF for 240, 360 and 900

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

    What's the Greatest Common Factor (GCF) of 240, 360 and 900?

    Answer

    GCF of 240, 360 and 900 is
    60

    (Sixty)

    60 is the largest positive integer that divides 240, 360 and 900 without a remainder — every other common divisor of the three divides it too.

    Finding the GCF of 240, 360 and 900 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 240: 2 × 2 × 2 × 2 × 3 × 5 (exponent form: 24 × 3 × 5)

    All Prime Factors of 360: 2 × 2 × 2 × 3 × 3 × 5 (exponent form: 23 × 32 × 5)

    All Prime Factors of 900: 2 × 2 × 3 × 3 × 5 × 5 (exponent form: 22 × 32 × 52)

    Prime factor240360900Lowest power
    224232222
    3332323
    555525

    GCF = 2 × 2 × 3 × 5 = 60

    Checking the GCF of 240, 360 and 900 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(240, 360) = 120

    GCF(120, 900) = 60

    GCF(240, 360, 900) = 60

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

    240 ÷ 60 = 4

    360 ÷ 60 = 6

    900 ÷ 60 = 15

    4, 6 and 15 have no common factor left — that is what makes 60 the greatest one.

    Related Calculations

    See Also

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    What is the GCF of 240, 360 and 900?. The GCF of 240, 360 and 900 is 60 — 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
    24036088515
    2403608862
    2403608871
    24036088824
    2403608891
    24036089010
    2403608913
    2403608924
    2403608931
    2403608946
    2403608955
    2403608968
    2403608973
    2403608982
    2403608991
    24036090060
    2403609011
    2403609022
    2403609033
    2403609048
    2403609055
    2403609066
    2403609071
    2403609084
    2403609093
    24036091010
    2403609111
    24036091224
    2403609131
    2403609142

    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 240, 360 and 900? (The answer is: 60). Enter the first number (e.g. '240'), the second (e.g. '360') and the third (e.g. '900'), 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 240, 360 and 900?

    GCF of 240, 360 and 900 is 60

    What prime factors do 240, 360 and 900 share?

    All three factorizations contain 2 × 2 × 3 × 5, and multiplying those shared primes gives 60 — exactly the greatest common factor.

    Can you get the GCF of 240, 360 and 900 two numbers at a time?

    Yes, and it is the check this page prints. The GCF of 240 and 360 is 120, and the GCF of 120 and 900 is 60 — 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 240 : 360 : 900?

    Divide every term by the GCF 60: 240 ÷ 60 = 4, 360 ÷ 60 = 6 and 900 ÷ 60 = 15. So 240 : 360 : 900 in lowest terms is 4 : 6 : 15, and no whole number other than 1 divides all three of those.

    See Also