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    GCF for 30, 60 and 90

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

    What's the Greatest Common Factor (GCF) of 30, 60 and 90?

    Answer

    GCF of 30, 60 and 90 is
    30

    (Thirty)

    30 is the largest positive integer that divides 30, 60 and 90 without a remainder — every other common divisor of the three divides it too.

    Finding the GCF of 30, 60 and 90 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 30: 2 × 3 × 5 (exponent form: 2 × 3 × 5)

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

    All Prime Factors of 90: 2 × 3 × 3 × 5 (exponent form: 2 × 32 × 5)

    Prime factor306090Lowest power
    222222
    333323
    55555

    GCF = 2 × 3 × 5 = 30

    Checking the GCF of 30, 60 and 90 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(30, 60) = 30

    GCF(30, 90) = 30

    GCF(30, 60, 90) = 30

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

    30 ÷ 30 = 1

    60 ÷ 30 = 2

    90 ÷ 30 = 3

    1, 2 and 3 have no common factor left — that is what makes 30 the greatest one.

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    What is the GCF of 30, 60 and 90?. The GCF of 30, 60 and 90 is 30 — 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
    30607515
    3060762
    3060771
    3060786
    3060791
    30608010
    3060813
    3060822
    3060831
    3060846
    3060855
    3060862
    3060873
    3060882
    3060891
    30609030
    3060911
    3060922
    3060933
    3060942
    3060955
    3060966
    3060971
    3060982
    3060993
    306010010
    30601011
    30601026
    30601031
    30601042

    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 30, 60 and 90? (The answer is: 30). Enter the first number (e.g. '30'), the second (e.g. '60') and the third (e.g. '90'), 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 30, 60 and 90?

    GCF of 30, 60 and 90 is 30

    What prime factors do 30, 60 and 90 share?

    All three factorizations contain 2 × 3 × 5, and multiplying those shared primes gives 30 — exactly the greatest common factor.

    Can you get the GCF of 30, 60 and 90 two numbers at a time?

    Yes, and it is the check this page prints. The GCF of 30 and 60 is 30, and the GCF of 30 and 90 is 30 — 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 30 : 60 : 90?

    Divide every term by the GCF 30: 30 ÷ 30 = 1, 60 ÷ 30 = 2 and 90 ÷ 30 = 3. So 30 : 60 : 90 in lowest terms is 1 : 2 : 3, and no whole number other than 1 divides all three of those.

    See Also