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    GCF for 18, 45 and 63

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

    What's the Greatest Common Factor (GCF) of 18, 45 and 63?

    Answer

    GCF of 18, 45 and 63 is
    9

    (Nine)

    9 is the largest positive integer that divides 18, 45 and 63 without a remainder — every other common divisor of the three divides it too.

    Finding the GCF of 18, 45 and 63 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 45: 3 × 3 × 5 (exponent form: 32 × 5)

    All Prime Factors of 63: 3 × 3 × 7 (exponent form: 32 × 7)

    Prime factor184563Lowest power
    22———
    332323232
    5—5——
    7——7—

    GCF = 3 × 3 = 9

    Checking the GCF of 18, 45 and 63 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, 45) = 9

    GCF(9, 63) = 9

    GCF(18, 45, 63) = 9

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

    18 ÷ 9 = 2

    45 ÷ 9 = 5

    63 ÷ 9 = 7

    2, 5 and 7 have no common factor left — that is what makes 9 the greatest one.

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    What is the GCF of 18, 45 and 63?. The GCF of 18, 45 and 63 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
    1845483
    1845491
    1845501
    1845513
    1845521
    1845531
    1845549
    1845551
    1845561
    1845573
    1845581
    1845591
    1845603
    1845611
    1845621
    1845639
    1845641
    1845651
    1845663
    1845671
    1845681
    1845693
    1845701
    1845711
    1845729
    1845731
    1845741
    1845753
    1845761
    1845771

    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, 45 and 63? (The answer is: 9). Enter the first number (e.g. '18'), the second (e.g. '45') and the third (e.g. '63'), 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, 45 and 63?

    GCF of 18, 45 and 63 is 9

    What prime factors do 18, 45 and 63 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, 45 and 63 two numbers at a time?

    Yes, and it is the check this page prints. The GCF of 18 and 45 is 9, and the GCF of 9 and 63 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 : 45 : 63?

    Divide every term by the GCF 9: 18 ÷ 9 = 2, 45 ÷ 9 = 5 and 63 ÷ 9 = 7. So 18 : 45 : 63 in lowest terms is 2 : 5 : 7, and no whole number other than 1 divides all three of those.

    See Also