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    GCF for 12, 21 and 30

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

    What's the Greatest Common Factor (GCF) of 12, 21 and 30?

    Answer

    GCF of 12, 21 and 30 is
    3

    (Three)

    3 is the largest positive integer that divides 12, 21 and 30 without a remainder — every other common divisor of the three divides it too.

    Finding the GCF of 12, 21 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 12: 2 × 2 × 3 (exponent form: 22 × 3)

    All Prime Factors of 21: 3 × 7 (exponent form: 3 × 7)

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

    Prime factor122130Lowest power
    222—2—
    33333
    5——5—
    7—7——

    GCF = 3 = 3

    Checking the GCF of 12, 21 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(12, 21) = 3

    GCF(3, 30) = 3

    GCF(12, 21, 30) = 3

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

    12 ÷ 3 = 4

    21 ÷ 3 = 7

    30 ÷ 3 = 10

    4, 7 and 10 have no common factor left — that is what makes 3 the greatest one.

    Related Calculations

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    What is the GCF of 12, 21 and 30?. The GCF of 12, 21 and 30 is 3 — 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
    1215213
    1216211
    1217211
    1218213
    1219211
    1220211
    1221213
    1221221
    1221231
    1221243
    1221251
    1221261
    1221273
    1221281
    1221291
    1221303
    1221311
    1221321
    1221333
    1221341
    1221351
    1221363
    1221371
    1221381
    1221393
    1221401
    1221411
    1221423
    1221431
    1221441

    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, 21 and 30? (The answer is: 3). Enter the first number (e.g. '12'), the second (e.g. '21') 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 12, 21 and 30?

    GCF of 12, 21 and 30 is 3

    What prime factors do 12, 21 and 30 share?

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

    Can you get the GCF of 12, 21 and 30 two numbers at a time?

    Yes, and it is the check this page prints. The GCF of 12 and 21 is 3, and the GCF of 3 and 30 is 3 — 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 : 21 : 30?

    Divide every term by the GCF 3: 12 ÷ 3 = 4, 21 ÷ 3 = 7 and 30 ÷ 3 = 10. So 12 : 21 : 30 in lowest terms is 4 : 7 : 10, and no whole number other than 1 divides all three of those.

    See Also