Mathematics · Greatest common factor
GCF of 6 and 8
The greatest common factor of 6 and 8 is 2. It is the largest whole number that divides both 6 and 8 with no remainder.
You will also see it written as the highest common factor (HCF) or the greatest common divisor (GCD) of 6 and 8. All three names mean the same thing.
Greatest common factor
2
GCF, GCD or HCF of 6 and 8
Least common multiple
24
LCM of 6 and 8
6/8 simplified
3/4
both divided by 2
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 6 and 8
Factors of 6: 1, 2, 3, 6
Factors of 8: 1, 2, 4, 8
Common factors: 1, 2
Greatest of those = 2
The common factors of 6 and 8 are 1 and 2, and that is the complete list. The largest one, 2, is the GCF.
Prime factorization method
6 = 2 × 3 (2 × 3)
8 = 23 (2 × 2 × 2)
Shared primes at their lowest power: 2
GCF = 2
Only 2 appears in both lists, and only once in each, so nothing else carries over and the GCF is 2.
Euclid's algorithm, step by step
8 ÷ 6 = 1 remainder 2
6 ÷ 2 = 3 remainder 0
Last non-zero remainder = 2, so the GCF is 2
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 6 and 8.
LCM of 6 and 8, and the fraction 6/8
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 = 2 × 24 = 48
6 × 8 = 48
They match, so both answers are right
Dividing the top and bottom of 6/8 by 2 reduces it to 3/4, which is as far as it goes. Anything smaller than the GCF would leave the fraction reducible.
Where these two numbers turn up
Six and eight share only a single 2, which is why 6/8 reduces to 3/4.
GCF of 6 and 8: FAQs
What is the GCF of 6 and 8?
The GCF of 6 and 8 is 2. It is the largest whole number that divides both of them exactly.
What are the common factors of 6 and 8?
The common factors of 6 and 8 are 1 and 2. The greatest of them is 2.
Is the GCF of 8 and 6 the same as the GCF of 6 and 8?
Yes. The order makes no difference. The greatest common factor of 8 and 6 is 2, exactly the same as the GCF of 6 and 8, 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 8 and 6.
What is the LCM of 6 and 8?
The LCM of 6 and 8 is 24. You can check it with GCF times LCM: 2 times 24 equals 48, which is the same as 6 times 8.
Are 6 and 8 coprime?
No. 6 and 8 share 2 as a common factor, so they are not coprime. Coprime numbers have a GCF of exactly 1.
How do you simplify 6/8?
Divide the top and the bottom by their GCF, which is 2. That gives 6 divided by 2 equals 3, and 8 divided by 2 equals 4, so 6/8 simplifies to 3/4.
Which method is quickest for 6 and 8?
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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