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    GCF for 18, 27 and 45

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

    What's the Greatest Common Factor (GCF) of 18, 27 and 45?

    Answer

    GCF of 18, 27 and 45 is
    9

    (Nine)

    9 is the largest positive integer that divides 18, 27 and 45 without a remainder — every other common divisor of the three divides it too.

    Finding the GCF of 18, 27 and 45 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 18: 2 × 3 × 3 (exponent form: 2 × 32)

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

    All Prime Factors of 45: 3 × 3 × 5 (exponent form: 32 × 5)

    Prime factor182745Lowest power
    22———
    332333232
    5——5—

    GCF = 3 × 3 = 9

    Checking the GCF of 18, 27 and 45 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(18, 27) = 9

    GCF(9, 45) = 9

    GCF(18, 27, 45) = 9

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

    18 ÷ 9 = 2

    27 ÷ 9 = 3

    45 ÷ 9 = 5

    2, 3 and 5 have no common factor left — that is what makes 9 the greatest one.

    Related Calculations

    See Also

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    What is the GCF of 18, 27 and 45?. The GCF of 18, 27 and 45 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
    1827303
    1827311
    1827321
    1827333
    1827341
    1827351
    1827369
    1827371
    1827381
    1827393
    1827401
    1827411
    1827423
    1827431
    1827441
    1827459
    1827461
    1827471
    1827483
    1827491
    1827501
    1827513
    1827521
    1827531
    1827549
    1827551
    1827561
    1827573
    1827581
    1827591

    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 18, 27 and 45? (The answer is: 9). Enter the first number (e.g. '18'), the second (e.g. '27') and the third (e.g. '45'), 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 18, 27 and 45?

    GCF of 18, 27 and 45 is 9

    What prime factors do 18, 27 and 45 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 18, 27 and 45 two numbers at a time?

    Yes, and it is the check this page prints. The GCF of 18 and 27 is 9, and the GCF of 9 and 45 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 18 : 27 : 45?

    Divide every term by the GCF 9: 18 ÷ 9 = 2, 27 ÷ 9 = 3 and 45 ÷ 9 = 5. So 18 : 27 : 45 in lowest terms is 2 : 3 : 5, and no whole number other than 1 divides all three of those.

    See Also