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    GCF for 12, 14 and 18

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

    What's the Greatest Common Factor (GCF) of 12, 14 and 18?

    Answer

    GCF of 12, 14 and 18 is
    2

    (Two)

    2 is the largest positive integer that divides 12, 14 and 18 without a remainder — every other common divisor of the three divides it too.

    Finding the GCF of 12, 14 and 18 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 12: 2 × 2 × 3 (exponent form: 22 × 3)

    All Prime Factors of 14: 2 × 7 (exponent form: 2 × 7)

    All Prime Factors of 18: 2 × 3 × 3 (exponent form: 2 × 32)

    Prime factor121418Lowest power
    222222
    33—32—
    7—7——

    GCF = 2 = 2

    Checking the GCF of 12, 14 and 18 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(12, 14) = 2

    GCF(2, 18) = 2

    GCF(12, 14, 18) = 2

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

    12 ÷ 2 = 6

    14 ÷ 2 = 7

    18 ÷ 2 = 9

    6, 7 and 9 have no common factor left — that is what makes 2 the greatest one.

    Related Calculations

    See Also

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    What is the GCF of 12, 14 and 18?. The GCF of 12, 14 and 18 is 2 — 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
    312141
    412142
    512141
    612142
    712141
    812142
    912141
    1012142
    1112141
    1212142
    1213141
    1214142
    1214151
    1214162
    1214171
    1214182
    1214191
    1214202
    1214211
    1214222
    1214231
    1214242
    1214251
    1214262
    1214271
    1214282
    1214291
    1214302
    1214311
    1214322

    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 12, 14 and 18? (The answer is: 2). Enter the first number (e.g. '12'), the second (e.g. '14') and the third (e.g. '18'), 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 12, 14 and 18?

    GCF of 12, 14 and 18 is 2

    What prime factors do 12, 14 and 18 share?

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

    Can you get the GCF of 12, 14 and 18 two numbers at a time?

    Yes, and it is the check this page prints. The GCF of 12 and 14 is 2, and the GCF of 2 and 18 is 2 — 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 12 : 14 : 18?

    Divide every term by the GCF 2: 12 ÷ 2 = 6, 14 ÷ 2 = 7 and 18 ÷ 2 = 9. So 12 : 14 : 18 in lowest terms is 6 : 7 : 9, and no whole number other than 1 divides all three of those.

    See Also