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    GCF for 18, 30 and 42

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

    What's the Greatest Common Factor (GCF) of 18, 30 and 42?

    Answer

    GCF of 18, 30 and 42 is
    6

    (Six)

    6 is the largest positive integer that divides 18, 30 and 42 without a remainder — every other common divisor of the three divides it too.

    Finding the GCF of 18, 30 and 42 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 30: 2 × 3 × 5 (exponent form: 2 × 3 × 5)

    All Prime Factors of 42: 2 × 3 × 7 (exponent form: 2 × 3 × 7)

    Prime factor183042Lowest power
    22222
    332333
    5—5——
    7——7—

    GCF = 2 × 3 = 6

    Checking the GCF of 18, 30 and 42 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, 30) = 6

    GCF(6, 42) = 6

    GCF(18, 30, 42) = 6

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

    18 ÷ 6 = 3

    30 ÷ 6 = 5

    42 ÷ 6 = 7

    3, 5 and 7 have no common factor left — that is what makes 6 the greatest one.

    Related Calculations

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    What is the GCF of 18, 30 and 42?. The GCF of 18, 30 and 42 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
    1827303
    1828302
    1829301
    1830306
    1830311
    1830322
    1830333
    1830342
    1830351
    1830366
    1830371
    1830382
    1830393
    1830402
    1830411
    1830426
    1830431
    1830442
    1830453
    1830462
    1830471
    1830486
    1830491
    1830502
    1830513
    1830522
    1830531
    1830546
    1830551
    1830562

    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, 30 and 42? (The answer is: 6). Enter the first number (e.g. '18'), the second (e.g. '30') and the third (e.g. '42'), 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, 30 and 42?

    GCF of 18, 30 and 42 is 6

    What prime factors do 18, 30 and 42 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, 30 and 42 two numbers at a time?

    Yes, and it is the check this page prints. The GCF of 18 and 30 is 6, and the GCF of 6 and 42 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 : 30 : 42?

    Divide every term by the GCF 6: 18 ÷ 6 = 3, 30 ÷ 6 = 5 and 42 ÷ 6 = 7. So 18 : 30 : 42 in lowest terms is 3 : 5 : 7, and no whole number other than 1 divides all three of those.

    See Also