GCF for 20, 30 and 40

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

What's the Greatest Common Factor (GCF) of 20, 30 and 40?

Answer

GCF of 20, 30 and 40 is
10

(Ten)

10 is the largest positive integer that divides 20, 30 and 40 without a remainder — every other common divisor of the three divides it too.

Finding the GCF of 20, 30 and 40 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 20: 2 × 2 × 5 (exponent form: 22 × 5)

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

All Prime Factors of 40: 2 × 2 × 2 × 5 (exponent form: 23 × 5)

Prime factor203040Lowest power
2222232
3—3——
55555

GCF = 2 × 5 = 10

Checking the GCF of 20, 30 and 40 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(20, 30) = 10

GCF(10, 40) = 10

GCF(20, 30, 40) = 10

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

20 ÷ 10 = 2

30 ÷ 10 = 3

40 ÷ 10 = 4

2, 3 and 4 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 20, 30 and 40? (The answer is: 10). Enter the first number (e.g. '20'), the second (e.g. '30') and the third (e.g. '40'), 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
2025305
2026302
2027301
2028302
2029301
20303010
2030311
2030322
2030331
2030342
2030355
2030362
2030371
2030382
2030391
20304010
2030411
2030422
2030431
2030442
2030455
2030462
2030471
2030482
2030491
20305010
2030511
2030522
2030531
2030542

FAQ

What's the Greatest Common Factor (GCF) of 20, 30 and 40?

GCF of 20, 30 and 40 is 10

What prime factors do 20, 30 and 40 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 20, 30 and 40 two numbers at a time?

Yes, and it is the check this page prints. The GCF of 20 and 30 is 10, and the GCF of 10 and 40 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 20 : 30 : 40?

Divide every term by the GCF 10: 20 ÷ 10 = 2, 30 ÷ 10 = 3 and 40 ÷ 10 = 4. So 20 : 30 : 40 in lowest terms is 2 : 3 : 4, and no whole number other than 1 divides all three of those.

See Also