GCF for 18, 32 and 48

"Greatest Common Factor of 3 Numbers" Calculator
Greatest Common Factor of
,
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What's the Greatest Common Factor (GCF) of 18, 32 and 48?

Answer

GCF of 18, 32 and 48 is
2

(Two)

2 is the largest positive integer that divides 18, 32 and 48 without a remainder — every other common divisor of the three divides it too.

Finding the GCF of 18, 32 and 48 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 18: 2 × 3 × 3 (exponent form: 2 × 32)

All Prime Factors of 32: 2 × 2 × 2 × 2 × 2 (exponent form: 25)

All Prime Factors of 48: 2 × 2 × 2 × 2 × 3 (exponent form: 24 × 3)

Prime factor183248Lowest power
2225242
332—3—

GCF = 2 = 2

Checking the GCF of 18, 32 and 48 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(18, 32) = 2

GCF(2, 48) = 2

GCF(18, 32, 48) = 2

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

18 ÷ 2 = 9

32 ÷ 2 = 16

48 ÷ 2 = 24

9, 16 and 24 have no common factor left — that is what makes 2 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 18, 32 and 48? (The answer is: 2). Enter the first number (e.g. '18'), the second (e.g. '32') and the third (e.g. '48'), 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
1832331
1832342
1832351
1832362
1832371
1832382
1832391
1832402
1832411
1832422
1832431
1832442
1832451
1832462
1832471
1832482
1832491
1832502
1832511
1832522
1832531
1832542
1832551
1832562
1832571
1832582
1832591
1832602
1832611
1832622

FAQ

What's the Greatest Common Factor (GCF) of 18, 32 and 48?

GCF of 18, 32 and 48 is 2

What prime factors do 18, 32 and 48 share?

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

Can you get the GCF of 18, 32 and 48 two numbers at a time?

Yes, and it is the check this page prints. The GCF of 18 and 32 is 2, and the GCF of 2 and 48 is 2 — 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 18 : 32 : 48?

Divide every term by the GCF 2: 18 ÷ 2 = 9, 32 ÷ 2 = 16 and 48 ÷ 2 = 24. So 18 : 32 : 48 in lowest terms is 9 : 16 : 24, and no whole number other than 1 divides all three of those.

See Also