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    GCF for 18, 24 and 30

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

    What's the Greatest Common Factor (GCF) of 18, 24 and 30?

    Answer

    GCF of 18, 24 and 30 is
    6

    (Six)

    6 is the largest positive integer that divides 18, 24 and 30 without a remainder — every other common divisor of the three divides it too.

    Finding the GCF of 18, 24 and 30 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 18: 2 × 3 × 3 (exponent form: 2 × 32)

    All Prime Factors of 24: 2 × 2 × 2 × 3 (exponent form: 23 × 3)

    All Prime Factors of 30: 2 × 3 × 5 (exponent form: 2 × 3 × 5)

    Prime factor182430Lowest power
    222322
    332333
    5——5—

    GCF = 2 × 3 = 6

    Checking the GCF of 18, 24 and 30 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(18, 24) = 6

    GCF(6, 30) = 6

    GCF(18, 24, 30) = 6

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

    18 ÷ 6 = 3

    24 ÷ 6 = 4

    30 ÷ 6 = 5

    3, 4 and 5 have no common factor left — that is what makes 6 the greatest one.

    Related Calculations

    See Also

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    What is the GCF of 18, 24 and 30?. The GCF of 18, 24 and 30 is 6 — 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
    1518243
    1618242
    1718241
    1818246
    1819241
    1820242
    1821243
    1822242
    1823241
    1824246
    1824251
    1824262
    1824273
    1824282
    1824291
    1824306
    1824311
    1824322
    1824333
    1824342
    1824351
    1824366
    1824371
    1824382
    1824393
    1824402
    1824411
    1824426
    1824431
    1824442

    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 18, 24 and 30? (The answer is: 6). Enter the first number (e.g. '18'), the second (e.g. '24') and the third (e.g. '30'), 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 18, 24 and 30?

    GCF of 18, 24 and 30 is 6

    What prime factors do 18, 24 and 30 share?

    All three factorizations contain 2 × 3, and multiplying those shared primes gives 6 — exactly the greatest common factor.

    Can you get the GCF of 18, 24 and 30 two numbers at a time?

    Yes, and it is the check this page prints. The GCF of 18 and 24 is 6, and the GCF of 6 and 30 is 6 — 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 18 : 24 : 30?

    Divide every term by the GCF 6: 18 ÷ 6 = 3, 24 ÷ 6 = 4 and 30 ÷ 6 = 5. So 18 : 24 : 30 in lowest terms is 3 : 4 : 5, and no whole number other than 1 divides all three of those.

    See Also