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    GCF for 18, 32 and 48

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

    What's the Greatest Common Factor (GCF) of 18, 32 and 48?

    Answer

    GCF of 18, 32 and 48 is
    2

    (Two)

    2 is the largest positive integer that divides 18, 32 and 48 without a remainder — every other common divisor of the three divides it too.

    Finding the GCF of 18, 32 and 48 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 32: 2 × 2 × 2 × 2 × 2 (exponent form: 25)

    All Prime Factors of 48: 2 × 2 × 2 × 2 × 3 (exponent form: 24 × 3)

    Prime factor183248Lowest power
    2225242
    332—3—

    GCF = 2 = 2

    Checking the GCF of 18, 32 and 48 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, 32) = 2

    GCF(2, 48) = 2

    GCF(18, 32, 48) = 2

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

    18 ÷ 2 = 9

    32 ÷ 2 = 16

    48 ÷ 2 = 24

    9, 16 and 24 have no common factor left — that is what makes 2 the greatest one.

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    What is the GCF of 18, 32 and 48?. The GCF of 18, 32 and 48 is 2 — 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
    1832331
    1832342
    1832351
    1832362
    1832371
    1832382
    1832391
    1832402
    1832411
    1832422
    1832431
    1832442
    1832451
    1832462
    1832471
    1832482
    1832491
    1832502
    1832511
    1832522
    1832531
    1832542
    1832551
    1832562
    1832571
    1832582
    1832591
    1832602
    1832611
    1832622

    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, 32 and 48? (The answer is: 2). Enter the first number (e.g. '18'), the second (e.g. '32') and the third (e.g. '48'), 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, 32 and 48?

    GCF of 18, 32 and 48 is 2

    What prime factors do 18, 32 and 48 share?

    All three factorizations contain 2, and multiplying those shared primes gives 2 — exactly the greatest common factor.

    Can you get the GCF of 18, 32 and 48 two numbers at a time?

    Yes, and it is the check this page prints. The GCF of 18 and 32 is 2, and the GCF of 2 and 48 is 2 — 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 : 32 : 48?

    Divide every term by the GCF 2: 18 ÷ 2 = 9, 32 ÷ 2 = 16 and 48 ÷ 2 = 24. So 18 : 32 : 48 in lowest terms is 9 : 16 : 24, and no whole number other than 1 divides all three of those.

    See Also