Mathematics · Greatest common factor
GCF of 36 and 54
The greatest common factor of 36 and 54 is 18. It is the largest whole number that divides both 36 and 54 with no remainder.
You will also see it written as the highest common factor (HCF) or the greatest common divisor (GCD) of 36 and 54. All three names mean the same thing.
Greatest common factor
18
GCF, GCD or HCF of 36 and 54
Least common multiple
108
LCM of 36 and 54
36/54 simplified
2/3
both divided by 18
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 36 and 54
Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
Factors of 54: 1, 2, 3, 6, 9, 18, 27, 54
Common factors: 1, 2, 3, 6, 9, 18
Greatest of those = 18
The common factors of 36 and 54 are 1, 2, 3, 6, 9 and 18, and that is the complete list. The largest one, 18, is the GCF.
Prime factorization method
36 = 22 × 32 (2 × 2 × 3 × 3)
54 = 2 × 33 (2 × 3 × 3 × 3)
Shared primes at their lowest power: 2 × 32
GCF = 18
Take every prime that appears in both lists, each at the lower of its two powers, and multiply them: 2 × 32 gives 18.
Euclid's algorithm, step by step
54 ÷ 36 = 1 remainder 18
36 ÷ 18 = 2 remainder 0
Last non-zero remainder = 18, so the GCF is 18
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 2 steps for 36 and 54.
LCM of 36 and 54, and the fraction 36/54
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 = 18 × 108 = 1,944
36 × 54 = 1,944
They match, so both answers are right
Dividing the top and bottom of 36/54 by 18 reduces it to 2/3, which is as far as it goes. Anything smaller than the GCF would leave the fraction reducible.
GCF of 36 and 54: FAQs
What is the GCF of 36 and 54?
The GCF of 36 and 54 is 18. It is the largest whole number that divides both of them exactly.
What are the common factors of 36 and 54?
The common factors of 36 and 54 are 1, 2, 3, 6, 9 and 18. The greatest of them is 18.
Is the GCF of 54 and 36 the same as the GCF of 36 and 54?
Yes. The order makes no difference. The greatest common factor of 54 and 36 is 18, exactly the same as the GCF of 36 and 54, 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 54 and 36.
What is the LCM of 36 and 54?
The LCM of 36 and 54 is 108. You can check it with GCF times LCM: 18 times 108 equals 1,944, which is the same as 36 times 54.
Are 36 and 54 coprime?
No. 36 and 54 share 18 as a common factor, so they are not coprime. Coprime numbers have a GCF of exactly 1.
How do you simplify 36/54?
Divide the top and the bottom by their GCF, which is 18. That gives 36 divided by 18 equals 2, and 54 divided by 18 equals 3, so 36/54 simplifies to 2/3.
Which method is quickest for 36 and 54?
Euclid's algorithm, because it reaches the answer in 2 steps and you never have to write out the full factor lists.
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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