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    GCF for 9, 18 and 27

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

    What's the Greatest Common Factor (GCF) of 9, 18 and 27?

    Answer

    GCF of 9, 18 and 27 is
    9

    (Nine)

    9 is the largest positive integer that divides 9, 18 and 27 without a remainder — every other common divisor of the three divides it too.

    Finding the GCF of 9, 18 and 27 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 18: 2 × 3 × 3 (exponent form: 2 × 32)

    All Prime Factors of 27: 3 × 3 × 3 (exponent form: 33)

    Prime factor91827Lowest power
    2—2——
    332323332

    GCF = 3 × 3 = 9

    Checking the GCF of 9, 18 and 27 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, 18) = 9

    GCF(9, 27) = 9

    GCF(9, 18, 27) = 9

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

    9 ÷ 9 = 1

    18 ÷ 9 = 2

    27 ÷ 9 = 3

    1, 2 and 3 have no common factor left — that is what makes 9 the greatest one.

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    What is the GCF of 9, 18 and 27?. The GCF of 9, 18 and 27 is 9 — 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
    912183
    913181
    914181
    915183
    916181
    917181
    918189
    918191
    918201
    918213
    918221
    918231
    918243
    918251
    918261
    918279
    918281
    918291
    918303
    918311
    918321
    918333
    918341
    918351
    918369
    918371
    918381
    918393
    918401
    918411

    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, 18 and 27? (The answer is: 9). Enter the first number (e.g. '9'), the second (e.g. '18') and the third (e.g. '27'), 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, 18 and 27?

    GCF of 9, 18 and 27 is 9

    What prime factors do 9, 18 and 27 share?

    All three factorizations contain 3 × 3, and multiplying those shared primes gives 9 — exactly the greatest common factor.

    Can you get the GCF of 9, 18 and 27 two numbers at a time?

    Yes, and it is the check this page prints. The GCF of 9 and 18 is 9, and the GCF of 9 and 27 is 9 — 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 : 18 : 27?

    Divide every term by the GCF 9: 9 ÷ 9 = 1, 18 ÷ 9 = 2 and 27 ÷ 9 = 3. So 9 : 18 : 27 in lowest terms is 1 : 2 : 3, and no whole number other than 1 divides all three of those.

    See Also