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    GCF for 4, 6 and 20

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

    What's the Greatest Common Factor (GCF) of 4, 6 and 20?

    Answer

    GCF of 4, 6 and 20 is
    2

    (Two)

    2 is the largest positive integer that divides 4, 6 and 20 without a remainder — every other common divisor of the three divides it too.

    Finding the GCF of 4, 6 and 20 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 4: 2 × 2 (exponent form: 22)

    All Prime Factors of 6: 2 × 3 (exponent form: 2 × 3)

    All Prime Factors of 20: 2 × 2 × 5 (exponent form: 22 × 5)

    Prime factor4620Lowest power
    2222222
    3—3——
    5——5—

    GCF = 2 = 2

    Checking the GCF of 4, 6 and 20 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(4, 6) = 2

    GCF(2, 20) = 2

    GCF(4, 6, 20) = 2

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

    4 ÷ 2 = 2

    6 ÷ 2 = 3

    20 ÷ 2 = 10

    2, 3 and 10 have no common factor left — that is what makes 2 the greatest one.

    Related Calculations

    See Also

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    What is the GCF of 4, 6 and 20?. The GCF of 4, 6 and 20 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
    4561
    4662
    4671
    4682
    4691
    46102
    46111
    46122
    46131
    46142
    46151
    46162
    46171
    46182
    46191
    46202
    46211
    46222
    46231
    46242
    46251
    46262
    46271
    46282
    46291
    46302
    46311
    46322
    46331
    46342

    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 4, 6 and 20? (The answer is: 2). Enter the first number (e.g. '4'), the second (e.g. '6') and the third (e.g. '20'), 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 4, 6 and 20?

    GCF of 4, 6 and 20 is 2

    What prime factors do 4, 6 and 20 share?

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

    Can you get the GCF of 4, 6 and 20 two numbers at a time?

    Yes, and it is the check this page prints. The GCF of 4 and 6 is 2, and the GCF of 2 and 20 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 4 : 6 : 20?

    Divide every term by the GCF 2: 4 ÷ 2 = 2, 6 ÷ 2 = 3 and 20 ÷ 2 = 10. So 4 : 6 : 20 in lowest terms is 2 : 3 : 10, and no whole number other than 1 divides all three of those.

    See Also