Mathematics · Greatest common factor
GCF of 9 and 18
The greatest common factor of 9 and 18 is 9. It is the largest whole number that divides both 9 and 18 with no remainder.
You will also see it written as the highest common factor (HCF) or the greatest common divisor (GCD) of 9 and 18. All three names mean the same thing.
Greatest common factor
9
GCF, GCD or HCF of 9 and 18
Least common multiple
18
LCM of 9 and 18
9/18 simplified
1/2
both divided by 9
Below is the same answer reached three different ways, because different classes teach different methods. Every line is worked out for these two numbers, so you can copy the one your teacher asks for.
Listing the factors of 9 and 18
Factors of 9: 1, 3, 9
Factors of 18: 1, 2, 3, 6, 9, 18
Common factors: 1, 3, 9
Greatest of those = 9
The common factors of 9 and 18 are 1, 3 and 9, and that is the complete list. The largest one, 9, is the GCF.
Prime factorization method
9 = 32 (3 × 3)
18 = 2 × 32 (2 × 3 × 3)
Shared primes at their lowest power: 32
GCF = 9
Take every prime that appears in both lists, each at the lower of its two powers, and multiply them: 32 gives 9.
Euclid's algorithm, step by step
18 ÷ 9 = 2 remainder 0
Last non-zero remainder = 9, so the GCF is 9
Divide the larger number by the smaller, then keep dividing the previous divisor by the remainder. When the remainder reaches zero, the divisor you used last is the GCF. It took 1 step for 9 and 18.
LCM of 9 and 18, and the fraction 9/18
For any two numbers, the GCF multiplied by the LCM equals the two numbers multiplied together. That gives a quick way to get one from the other, and a way to check both.
GCF × LCM = 9 × 18 = 162
9 × 18 = 162
They match, so both answers are right
Dividing the top and bottom of 9/18 by 9 reduces it to 1/2, which is as far as it goes. Anything smaller than the GCF would leave the fraction reducible.
Where these two numbers turn up
Eighteen is exactly double nine, so the smaller number is itself the GCF.
GCF of 9 and 18: FAQs
What is the GCF of 9 and 18?
The GCF of 9 and 18 is 9. It is the largest whole number that divides both of them exactly.
What are the common factors of 9 and 18?
The common factors of 9 and 18 are 1, 3 and 9. The greatest of them is 9.
Is the GCF of 18 and 9 the same as the GCF of 9 and 18?
Yes. The order makes no difference. The greatest common factor of 18 and 9 is 9, exactly the same as the GCF of 9 and 18, because you are looking at the same two numbers either way. The same is true if you see it written as the highest common factor of 18 and 9.
What is the LCM of 9 and 18?
The LCM of 9 and 18 is 18. You can check it with GCF times LCM: 9 times 18 equals 162, which is the same as 9 times 18.
Are 9 and 18 coprime?
No. 9 and 18 share 9 as a common factor, so they are not coprime. Coprime numbers have a GCF of exactly 1.
How do you simplify 9/18?
Divide the top and the bottom by their GCF, which is 9. That gives 9 divided by 9 equals 1, and 18 divided by 9 equals 2, so 9/18 simplifies to 1/2.
Which method is quickest for 9 and 18?
Listing factors, because both numbers are small enough to write the factors out by eye.
Nearby pairs
Any other numbers? The GCF Calculator takes two to ten values and shows the same three methods, and the math calculators page has the rest of the set.
Open the GCF Calculator →
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