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    GCF for 10, 12 and 15

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

    What's the Greatest Common Factor (GCF) of 10, 12 and 15?

    Answer

    GCF of 10, 12 and 15 is
    1

    (One)

    1 is the largest positive integer that divides 10, 12 and 15 without a remainder — every other common divisor of the three divides it too.

    Finding the GCF of 10, 12 and 15 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 10: 2 × 5 (exponent form: 2 × 5)

    All Prime Factors of 12: 2 × 2 × 3 (exponent form: 22 × 3)

    All Prime Factors of 15: 3 × 5 (exponent form: 3 × 5)

    Prime factor101215Lowest power
    2222——
    3—33—
    55—5—

    Not one prime factor is shared by all three numbers, which makes 10, 12 and 15 relatively prime as a set. The only positive integer dividing all of them is 1.

    Checking the GCF of 10, 12 and 15 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(10, 12) = 2

    GCF(2, 15) = 1

    GCF(10, 12, 15) = 1

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

    10 ÷ 1 = 10

    12 ÷ 1 = 12

    15 ÷ 1 = 15

    10, 12 and 15 have no common factor left — that is what makes 1 the greatest one.

    Related Calculations

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    What is the GCF of 10, 12 and 15?. The GCF of 10, 12 and 15 is 1 — 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
    110121
    210122
    310121
    410122
    510121
    610122
    710121
    810122
    910121
    1010122
    1011121
    1012122
    1012131
    1012142
    1012151
    1012162
    1012171
    1012182
    1012191
    1012202
    1012211
    1012222
    1012231
    1012242
    1012251
    1012262
    1012271
    1012282
    1012291
    1012302

    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 10, 12 and 15? (The answer is: 1). Enter the first number (e.g. '10'), the second (e.g. '12') and the third (e.g. '15'), 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 10, 12 and 15?

    GCF of 10, 12 and 15 is 1

    What prime factors do 10, 12 and 15 share?

    None at all: 10, 12 and 15 have no prime factor in common, so the only positive integer dividing all three is 1 and their GCF is 1.

    Can you get the GCF of 10, 12 and 15 two numbers at a time?

    Yes, and it is the check this page prints. The GCF of 10 and 12 is 2, and the GCF of 2 and 15 is 1 — 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 10 : 12 : 15?

    Divide every term by the GCF 1: 10 ÷ 1 = 10, 12 ÷ 1 = 12 and 15 ÷ 1 = 15. So 10 : 12 : 15 in lowest terms is 10 : 12 : 15, and no whole number other than 1 divides all three of those.

    See Also