GCF for 240, 360 and 900

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

What's the Greatest Common Factor (GCF) of 240, 360 and 900?

Answer

GCF of 240, 360 and 900 is
60

(Sixty)

60 is the largest positive integer that divides 240, 360 and 900 without a remainder — every other common divisor of the three divides it too.

Finding the GCF of 240, 360 and 900 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 240: 2 × 2 × 2 × 2 × 3 × 5 (exponent form: 24 × 3 × 5)

All Prime Factors of 360: 2 × 2 × 2 × 3 × 3 × 5 (exponent form: 23 × 32 × 5)

All Prime Factors of 900: 2 × 2 × 3 × 3 × 5 × 5 (exponent form: 22 × 32 × 52)

Prime factor240360900Lowest power
224232222
3332323
555525

GCF = 2 × 2 × 3 × 5 = 60

Checking the GCF of 240, 360 and 900 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(240, 360) = 120

GCF(120, 900) = 60

GCF(240, 360, 900) = 60

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

240 ÷ 60 = 4

360 ÷ 60 = 6

900 ÷ 60 = 15

4, 6 and 15 have no common factor left — that is what makes 60 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 240, 360 and 900? (The answer is: 60). Enter the first number (e.g. '240'), the second (e.g. '360') and the third (e.g. '900'), 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
24036088515
2403608862
2403608871
24036088824
2403608891
24036089010
2403608913
2403608924
2403608931
2403608946
2403608955
2403608968
2403608973
2403608982
2403608991
24036090060
2403609011
2403609022
2403609033
2403609048
2403609055
2403609066
2403609071
2403609084
2403609093
24036091010
2403609111
24036091224
2403609131
2403609142

FAQ

What's the Greatest Common Factor (GCF) of 240, 360 and 900?

GCF of 240, 360 and 900 is 60

What prime factors do 240, 360 and 900 share?

All three factorizations contain 2 × 2 × 3 × 5, and multiplying those shared primes gives 60 — exactly the greatest common factor.

Can you get the GCF of 240, 360 and 900 two numbers at a time?

Yes, and it is the check this page prints. The GCF of 240 and 360 is 120, and the GCF of 120 and 900 is 60 — 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 240 : 360 : 900?

Divide every term by the GCF 60: 240 ÷ 60 = 4, 360 ÷ 60 = 6 and 900 ÷ 60 = 15. So 240 : 360 : 900 in lowest terms is 4 : 6 : 15, and no whole number other than 1 divides all three of those.

See Also