GCF for 24, 36 and 60

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

What's the Greatest Common Factor (GCF) of 24, 36 and 60?

Answer

GCF of 24, 36 and 60 is
12

(Twelve)

12 is the largest positive integer that divides 24, 36 and 60 without a remainder — every other common divisor of the three divides it too.

Finding the GCF of 24, 36 and 60 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 24: 2 × 2 × 2 × 3 (exponent form: 23 × 3)

All Prime Factors of 36: 2 × 2 × 3 × 3 (exponent form: 22 × 32)

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

Prime factor243660Lowest power
223222222
333233
5——5—

GCF = 2 × 2 × 3 = 12

Checking the GCF of 24, 36 and 60 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(24, 36) = 12

GCF(12, 60) = 12

GCF(24, 36, 60) = 12

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

24 ÷ 12 = 2

36 ÷ 12 = 3

60 ÷ 12 = 5

2, 3 and 5 have no common factor left — that is what makes 12 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 24, 36 and 60? (The answer is: 12). Enter the first number (e.g. '24'), the second (e.g. '36') and the third (e.g. '60'), 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
2436453
2436462
2436471
24364812
2436491
2436502
2436513
2436524
2436531
2436546
2436551
2436564
2436573
2436582
2436591
24366012
2436611
2436622
2436633
2436644
2436651
2436666
2436671
2436684
2436693
2436702
2436711
24367212
2436731
2436742

FAQ

What's the Greatest Common Factor (GCF) of 24, 36 and 60?

GCF of 24, 36 and 60 is 12

What prime factors do 24, 36 and 60 share?

All three factorizations contain 2 × 2 × 3, and multiplying those shared primes gives 12 — exactly the greatest common factor.

Can you get the GCF of 24, 36 and 60 two numbers at a time?

Yes, and it is the check this page prints. The GCF of 24 and 36 is 12, and the GCF of 12 and 60 is 12 — 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 24 : 36 : 60?

Divide every term by the GCF 12: 24 ÷ 12 = 2, 36 ÷ 12 = 3 and 60 ÷ 12 = 5. So 24 : 36 : 60 in lowest terms is 2 : 3 : 5, and no whole number other than 1 divides all three of those.

See Also