GCF for 45, 81 and 99

"Greatest Common Factor of 3 Numbers" Calculator
Greatest Common Factor of
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What's the Greatest Common Factor (GCF) of 45, 81 and 99?

Answer

GCF of 45, 81 and 99 is
9

(Nine)

9 is the largest positive integer that divides 45, 81 and 99 without a remainder — every other common divisor of the three divides it too.

Finding the GCF of 45, 81 and 99 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 45: 3 × 3 × 5 (exponent form: 32 × 5)

All Prime Factors of 81: 3 × 3 × 3 × 3 (exponent form: 34)

All Prime Factors of 99: 3 × 3 × 11 (exponent form: 32 × 11)

Prime factor458199Lowest power
332343232
55———
11——11—

GCF = 3 × 3 = 9

Checking the GCF of 45, 81 and 99 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(45, 81) = 9

GCF(9, 99) = 9

GCF(45, 81, 99) = 9

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

45 ÷ 9 = 5

81 ÷ 9 = 9

99 ÷ 9 = 11

5, 9 and 11 have no common factor left — that is what makes 9 the greatest one.

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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 45, 81 and 99? (The answer is: 9). Enter the first number (e.g. '45'), the second (e.g. '81') and the third (e.g. '99'), 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
4581843
4581851
4581861
4581873
4581881
4581891
4581909
4581911
4581921
4581933
4581941
4581951
4581963
4581971
4581981
4581999
45811001
45811011
45811023
45811031
45811041
45811053
45811061
45811071
45811089
45811091
45811101
45811113
45811121
45811131

FAQ

What's the Greatest Common Factor (GCF) of 45, 81 and 99?

GCF of 45, 81 and 99 is 9

What prime factors do 45, 81 and 99 share?

All three factorizations contain 3 × 3, and multiplying those shared primes gives 9 — exactly the greatest common factor.

Can you get the GCF of 45, 81 and 99 two numbers at a time?

Yes, and it is the check this page prints. The GCF of 45 and 81 is 9, and the GCF of 9 and 99 is 9 — 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 45 : 81 : 99?

Divide every term by the GCF 9: 45 ÷ 9 = 5, 81 ÷ 9 = 9 and 99 ÷ 9 = 11. So 45 : 81 : 99 in lowest terms is 5 : 9 : 11, and no whole number other than 1 divides all three of those.

See Also