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    GCF for 9, 15 and 18

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

    What's the Greatest Common Factor (GCF) of 9, 15 and 18?

    Answer

    GCF of 9, 15 and 18 is
    3

    (Three)

    3 is the largest positive integer that divides 9, 15 and 18 without a remainder — every other common divisor of the three divides it too.

    Finding the GCF of 9, 15 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 9: 3 × 3 (exponent form: 32)

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

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

    Prime factor91518Lowest power
    2——2—
    3323323
    5—5——

    GCF = 3 = 3

    Checking the GCF of 9, 15 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(9, 15) = 3

    GCF(3, 18) = 3

    GCF(9, 15, 18) = 3

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

    9 ÷ 3 = 3

    15 ÷ 3 = 5

    18 ÷ 3 = 6

    3, 5 and 6 have no common factor left — that is what makes 3 the greatest one.

    Related Calculations

    See Also

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    What is the GCF of 9, 15 and 18?. The GCF of 9, 15 and 18 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
    39153
    49151
    59151
    69153
    79151
    89151
    99153
    910151
    911151
    912153
    913151
    914151
    915153
    915161
    915171
    915183
    915191
    915201
    915213
    915221
    915231
    915243
    915251
    915261
    915273
    915281
    915291
    915303
    915311
    915321

    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 9, 15 and 18? (The answer is: 3). Enter the first number (e.g. '9'), the second (e.g. '15') 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 9, 15 and 18?

    GCF of 9, 15 and 18 is 3

    What prime factors do 9, 15 and 18 share?

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

    Can you get the GCF of 9, 15 and 18 two numbers at a time?

    Yes, and it is the check this page prints. The GCF of 9 and 15 is 3, and the GCF of 3 and 18 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 9 : 15 : 18?

    Divide every term by the GCF 3: 9 ÷ 3 = 3, 15 ÷ 3 = 5 and 18 ÷ 3 = 6. So 9 : 15 : 18 in lowest terms is 3 : 5 : 6, and no whole number other than 1 divides all three of those.

    See Also