GCF for 40, 60 and 100

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

What's the Greatest Common Factor (GCF) of 40, 60 and 100?

Answer

GCF of 40, 60 and 100 is
20

(Twenty)

20 is the largest positive integer that divides 40, 60 and 100 without a remainder — every other common divisor of the three divides it too.

Finding the GCF of 40, 60 and 100 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 40: 2 × 2 × 2 × 5 (exponent form: 23 × 5)

All Prime Factors of 60: 2 × 2 × 3 × 5 (exponent form: 22 × 3 × 5)

All Prime Factors of 100: 2 × 2 × 5 × 5 (exponent form: 22 × 52)

Prime factor4060100Lowest power
223222222
3—3——
555525

GCF = 2 × 2 × 5 = 20

Checking the GCF of 40, 60 and 100 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(40, 60) = 20

GCF(20, 100) = 20

GCF(40, 60, 100) = 20

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

40 ÷ 20 = 2

60 ÷ 20 = 3

100 ÷ 20 = 5

2, 3 and 5 have no common factor left — that is what makes 20 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 40, 60 and 100? (The answer is: 20). Enter the first number (e.g. '40'), the second (e.g. '60') and the third (e.g. '100'), 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
4060855
4060862
4060871
4060884
4060891
40609010
4060911
4060924
4060931
4060942
4060955
4060964
4060971
4060982
4060991
406010020
40601011
40601022
40601031
40601044
40601055
40601062
40601071
40601084
40601091
406011010
40601111
40601124
40601131
40601142

FAQ

What's the Greatest Common Factor (GCF) of 40, 60 and 100?

GCF of 40, 60 and 100 is 20

What prime factors do 40, 60 and 100 share?

All three factorizations contain 2 × 2 × 5, and multiplying those shared primes gives 20 — exactly the greatest common factor.

Can you get the GCF of 40, 60 and 100 two numbers at a time?

Yes, and it is the check this page prints. The GCF of 40 and 60 is 20, and the GCF of 20 and 100 is 20 — 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 40 : 60 : 100?

Divide every term by the GCF 20: 40 ÷ 20 = 2, 60 ÷ 20 = 3 and 100 ÷ 20 = 5. So 40 : 60 : 100 in lowest terms is 2 : 3 : 5, and no whole number other than 1 divides all three of those.

See Also