Mathematics · Greatest common factor
GCF of 12 and 15
The greatest common factor of 12 and 15 is 3. It is the largest whole number that divides both 12 and 15 with no remainder.
You will also see it written as the highest common factor (HCF) or the greatest common divisor (GCD) of 12 and 15. All three names mean the same thing.
Greatest common factor
3
GCF, GCD or HCF of 12 and 15
Least common multiple
60
LCM of 12 and 15
12/15 simplified
4/5
both divided by 3
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 12 and 15
Factors of 12: 1, 2, 3, 4, 6, 12
Factors of 15: 1, 3, 5, 15
Common factors: 1, 3
Greatest of those = 3
The common factors of 12 and 15 are 1 and 3, and that is the complete list. The largest one, 3, is the GCF.
Prime factorization method
12 = 22 × 3 (2 × 2 × 3)
15 = 3 × 5 (3 × 5)
Shared primes at their lowest power: 3
GCF = 3
Only 3 appears in both lists, and only once in each, so nothing else carries over and the GCF is 3.
Euclid's algorithm, step by step
15 ÷ 12 = 1 remainder 3
12 ÷ 3 = 4 remainder 0
Last non-zero remainder = 3, so the GCF is 3
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 12 and 15.
LCM of 12 and 15, and the fraction 12/15
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 = 3 × 60 = 180
12 × 15 = 180
They match, so both answers are right
Dividing the top and bottom of 12/15 by 3 reduces it to 4/5, which is as far as it goes. Anything smaller than the GCF would leave the fraction reducible.
GCF of 12 and 15: FAQs
What is the GCF of 12 and 15?
The GCF of 12 and 15 is 3. It is the largest whole number that divides both of them exactly.
What are the common factors of 12 and 15?
The common factors of 12 and 15 are 1 and 3. The greatest of them is 3.
Is the GCF of 15 and 12 the same as the GCF of 12 and 15?
Yes. The order makes no difference. The greatest common factor of 15 and 12 is 3, exactly the same as the GCF of 12 and 15, 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 15 and 12.
What is the LCM of 12 and 15?
The LCM of 12 and 15 is 60. You can check it with GCF times LCM: 3 times 60 equals 180, which is the same as 12 times 15.
Are 12 and 15 coprime?
No. 12 and 15 share 3 as a common factor, so they are not coprime. Coprime numbers have a GCF of exactly 1.
How do you simplify 12/15?
Divide the top and the bottom by their GCF, which is 3. That gives 12 divided by 3 equals 4, and 15 divided by 3 equals 5, so 12/15 simplifies to 4/5.
Which method is quickest for 12 and 15?
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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