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    GCF for 12, 15 and 21

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

    What's the Greatest Common Factor (GCF) of 12, 15 and 21?

    Answer

    GCF of 12, 15 and 21 is
    3

    (Three)

    3 is the largest positive integer that divides 12, 15 and 21 without a remainder — every other common divisor of the three divides it too.

    Finding the GCF of 12, 15 and 21 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 15: 3 × 5 (exponent form: 3 × 5)

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

    Prime factor121521Lowest power
    222———
    33333
    5—5——
    7——7—

    GCF = 3 = 3

    Checking the GCF of 12, 15 and 21 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, 15) = 3

    GCF(3, 21) = 3

    GCF(12, 15, 21) = 3

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

    12 ÷ 3 = 4

    15 ÷ 3 = 5

    21 ÷ 3 = 7

    4, 5 and 7 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, 15 and 21?. The GCF of 12, 15 and 21 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
    612153
    712151
    812151
    912153
    1012151
    1112151
    1212153
    1213151
    1214151
    1215153
    1215161
    1215171
    1215183
    1215191
    1215201
    1215213
    1215221
    1215231
    1215243
    1215251
    1215261
    1215273
    1215281
    1215291
    1215303
    1215311
    1215321
    1215333
    1215341
    1215351

    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, 15 and 21? (The answer is: 3). Enter the first number (e.g. '12'), the second (e.g. '15') and the third (e.g. '21'), 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, 15 and 21?

    GCF of 12, 15 and 21 is 3

    What prime factors do 12, 15 and 21 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, 15 and 21 two numbers at a time?

    Yes, and it is the check this page prints. The GCF of 12 and 15 is 3, and the GCF of 3 and 21 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 : 15 : 21?

    Divide every term by the GCF 3: 12 ÷ 3 = 4, 15 ÷ 3 = 5 and 21 ÷ 3 = 7. So 12 : 15 : 21 in lowest terms is 4 : 5 : 7, and no whole number other than 1 divides all three of those.

    See Also