Feedback form
Hi! What do you think?

Drag it here or paste with Ctrl+V

    You can also email us on infocalculat.io

    GCF for 3, 6 and 8

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

    What's the Greatest Common Factor (GCF) of 3, 6 and 8?

    Answer

    GCF of 3, 6 and 8 is
    1

    (One)

    1 is the largest positive integer that divides 3, 6 and 8 without a remainder — every other common divisor of the three divides it too.

    Finding the GCF of 3, 6 and 8 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 3: 3 (exponent form: 3)

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

    All Prime Factors of 8: 2 × 2 × 2 (exponent form: 23)

    Prime factor368Lowest power
    2—223—
    333——

    Not one prime factor is shared by all three numbers, which makes 3, 6 and 8 relatively prime as a set. The only positive integer dividing all of them is 1.

    Checking the GCF of 3, 6 and 8 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(3, 6) = 3

    GCF(3, 8) = 1

    GCF(3, 6, 8) = 1

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

    3 ÷ 1 = 3

    6 ÷ 1 = 6

    8 ÷ 1 = 8

    3, 6 and 8 have no common factor left — that is what makes 1 the greatest one.

    Related Calculations

    See Also

    Share This Calculation
    Print
    https://calculat.io/en/number/greatest-common-factor-of-3-numbers/3--6--8Copy
    <a href="https://calculat.io/en/number/greatest-common-factor-of-3-numbers/3--6--8">What is the GCF of 3, 6 and 8? - Calculatio</a>Copy
    Facebook
    Twitter
    Telegram
    WhatsApp
    Viber
    Email
    What is the GCF of 3, 6 and 8?. The GCF of 3, 6 and 8 is 1 — the largest number that divides all three with no remainder. Step-by-step solution for three numbers.
    https://calculat.io/en/number/greatest-common-factor-of-3-numbers/3--6--8/generated.jpgCopy

    GCF Table

    Number 1Number 2Number 3GCF
    1361
    2361
    3363
    3461
    3561
    3663
    3671
    3681
    3693
    36101
    36111
    36123
    36131
    36141
    36153
    36161
    36171
    36183
    36191
    36201
    36213
    36221
    36231
    36243
    36251
    36261
    36273
    36281
    36291
    36303

    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 3, 6 and 8? (The answer is: 1). Enter the first number (e.g. '3'), the second (e.g. '6') and the third (e.g. '8'), 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 3, 6 and 8?

    GCF of 3, 6 and 8 is 1

    What prime factors do 3, 6 and 8 share?

    None at all: 3, 6 and 8 have no prime factor in common, so the only positive integer dividing all three is 1 and their GCF is 1.

    Can you get the GCF of 3, 6 and 8 two numbers at a time?

    Yes, and it is the check this page prints. The GCF of 3 and 6 is 3, and the GCF of 3 and 8 is 1 — 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 3 : 6 : 8?

    Divide every term by the GCF 1: 3 ÷ 1 = 3, 6 ÷ 1 = 6 and 8 ÷ 1 = 8. So 3 : 6 : 8 in lowest terms is 3 : 6 : 8, and no whole number other than 1 divides all three of those.

    See Also