GCF for 10, 20 and 30

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

What's the Greatest Common Factor (GCF) of 10, 20 and 30?

Answer

GCF of 10, 20 and 30 is
10

(Ten)

10 is the largest positive integer that divides 10, 20 and 30 without a remainder — every other common divisor of the three divides it too.

Finding the GCF of 10, 20 and 30 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 10: 2 × 5 (exponent form: 2 × 5)

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

All Prime Factors of 30: 2 × 3 × 5 (exponent form: 2 × 3 × 5)

Prime factor102030Lowest power
222222
3——3—
55555

GCF = 2 × 5 = 10

Checking the GCF of 10, 20 and 30 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(10, 20) = 10

GCF(10, 30) = 10

GCF(10, 20, 30) = 10

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

10 ÷ 10 = 1

20 ÷ 10 = 2

30 ÷ 10 = 3

1, 2 and 3 have no common factor left — that is what makes 10 the greatest one.

Related Calculations

See Also

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 10, 20 and 30? (The answer is: 10). Enter the first number (e.g. '10'), the second (e.g. '20') and the third (e.g. '30'), 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

GCF Table

Number 1Number 2Number 3GCF
1015205
1016202
1017201
1018202
1019201
10202010
1020211
1020222
1020231
1020242
1020255
1020262
1020271
1020282
1020291
10203010
1020311
1020322
1020331
1020342
1020355
1020362
1020371
1020382
1020391
10204010
1020411
1020422
1020431
1020442

FAQ

What's the Greatest Common Factor (GCF) of 10, 20 and 30?

GCF of 10, 20 and 30 is 10

What prime factors do 10, 20 and 30 share?

All three factorizations contain 2 × 5, and multiplying those shared primes gives 10 — exactly the greatest common factor.

Can you get the GCF of 10, 20 and 30 two numbers at a time?

Yes, and it is the check this page prints. The GCF of 10 and 20 is 10, and the GCF of 10 and 30 is 10 — 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 10 : 20 : 30?

Divide every term by the GCF 10: 10 ÷ 10 = 1, 20 ÷ 10 = 2 and 30 ÷ 10 = 3. So 10 : 20 : 30 in lowest terms is 1 : 2 : 3, and no whole number other than 1 divides all three of those.

See Also