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    GCF for 6, 10 and 15

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

    What's the Greatest Common Factor (GCF) of 6, 10 and 15?

    Answer

    GCF of 6, 10 and 15 is
    1

    (One)

    1 is the largest positive integer that divides 6, 10 and 15 without a remainder — every other common divisor of the three divides it too.

    Finding the GCF of 6, 10 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 6: 2 × 3 (exponent form: 2 × 3)

    All Prime Factors of 10: 2 × 5 (exponent form: 2 × 5)

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

    Prime factor61015Lowest power
    222——
    33—3—
    5—55—

    Not one prime factor is shared by all three numbers, which makes 6, 10 and 15 relatively prime as a set. The only positive integer dividing all of them is 1.

    Checking the GCF of 6, 10 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(6, 10) = 2

    GCF(2, 15) = 1

    GCF(6, 10, 15) = 1

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

    6 ÷ 1 = 6

    10 ÷ 1 = 10

    15 ÷ 1 = 15

    6, 10 and 15 have no common factor left — that is what makes 1 the greatest one.

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    See Also

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    What is the GCF of 6, 10 and 15?. The GCF of 6, 10 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
    16101
    26102
    36101
    46102
    56101
    66102
    67101
    68102
    69101
    610102
    610111
    610122
    610131
    610142
    610151
    610162
    610171
    610182
    610191
    610202
    610211
    610222
    610231
    610242
    610251
    610262
    610271
    610282
    610291
    610302

    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 6, 10 and 15? (The answer is: 1). Enter the first number (e.g. '6'), the second (e.g. '10') 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 6, 10 and 15?

    GCF of 6, 10 and 15 is 1

    What prime factors do 6, 10 and 15 share?

    None at all: 6, 10 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 6, 10 and 15 two numbers at a time?

    Yes, and it is the check this page prints. The GCF of 6 and 10 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 6 : 10 : 15?

    Divide every term by the GCF 1: 6 ÷ 1 = 6, 10 ÷ 1 = 10 and 15 ÷ 1 = 15. So 6 : 10 : 15 in lowest terms is 6 : 10 : 15, and no whole number other than 1 divides all three of those.

    See Also