Mathematics · Greatest common factor
GCF of 8 and 12
The greatest common factor of 8 and 12 is 4. It is the largest whole number that divides both 8 and 12 with no remainder.
You will also see it written as the highest common factor (HCF) or the greatest common divisor (GCD) of 8 and 12. All three names mean the same thing.
Greatest common factor
4
GCF, GCD or HCF of 8 and 12
Least common multiple
24
LCM of 8 and 12
8/12 simplified
2/3
both divided by 4
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 8 and 12
Factors of 8: 1, 2, 4, 8
Factors of 12: 1, 2, 3, 4, 6, 12
Common factors: 1, 2, 4
Greatest of those = 4
The common factors of 8 and 12 are 1, 2 and 4, and that is the complete list. The largest one, 4, is the GCF.
Prime factorization method
8 = 23 (2 × 2 × 2)
12 = 22 × 3 (2 × 2 × 3)
Shared primes at their lowest power: 22
GCF = 4
Take every prime that appears in both lists, each at the lower of its two powers, and multiply them: 22 gives 4.
Euclid's algorithm, step by step
12 ÷ 8 = 1 remainder 4
8 ÷ 4 = 2 remainder 0
Last non-zero remainder = 4, so the GCF is 4
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 8 and 12.
LCM of 8 and 12, and the fraction 8/12
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 = 4 × 24 = 96
8 × 12 = 96
They match, so both answers are right
Dividing the top and bottom of 8/12 by 4 reduces it to 2/3, which is as far as it goes. Anything smaller than the GCF would leave the fraction reducible.
Where these two numbers turn up
Egg boxes come in eights and twelves, and both split into identical groups of 4, which is the GCF.
GCF of 8 and 12: FAQs
What is the GCF of 8 and 12?
The GCF of 8 and 12 is 4. It is the largest whole number that divides both of them exactly.
What are the common factors of 8 and 12?
The common factors of 8 and 12 are 1, 2 and 4. The greatest of them is 4.
Is the GCF of 12 and 8 the same as the GCF of 8 and 12?
Yes. The order makes no difference. The greatest common factor of 12 and 8 is 4, exactly the same as the GCF of 8 and 12, 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 12 and 8.
What is the LCM of 8 and 12?
The LCM of 8 and 12 is 24. You can check it with GCF times LCM: 4 times 24 equals 96, which is the same as 8 times 12.
Are 8 and 12 coprime?
No. 8 and 12 share 4 as a common factor, so they are not coprime. Coprime numbers have a GCF of exactly 1.
How do you simplify 8/12?
Divide the top and the bottom by their GCF, which is 4. That gives 8 divided by 4 equals 2, and 12 divided by 4 equals 3, so 8/12 simplifies to 2/3.
Which method is quickest for 8 and 12?
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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