Mathematics · Greatest common factor
GCF of 8 and 16
The greatest common factor of 8 and 16 is 8. It is the largest whole number that divides both 8 and 16 with no remainder.
You will also see it written as the highest common factor (HCF) or the greatest common divisor (GCD) of 8 and 16. All three names mean the same thing.
Greatest common factor
8
GCF, GCD or HCF of 8 and 16
Least common multiple
16
LCM of 8 and 16
8/16 simplified
1/2
both divided by 8
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 16
Factors of 8: 1, 2, 4, 8
Factors of 16: 1, 2, 4, 8, 16
Common factors: 1, 2, 4, 8
Greatest of those = 8
The common factors of 8 and 16 are 1, 2, 4 and 8, and that is the complete list. The largest one, 8, is the GCF.
Prime factorization method
8 = 23 (2 × 2 × 2)
16 = 24 (2 × 2 × 2 × 2)
Shared primes at their lowest power: 23
GCF = 8
Take every prime that appears in both lists, each at the lower of its two powers, and multiply them: 23 gives 8.
Euclid's algorithm, step by step
16 ÷ 8 = 2 remainder 0
Last non-zero remainder = 8, so the GCF is 8
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 8 and 16.
LCM of 8 and 16, and the fraction 8/16
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 = 8 × 16 = 128
8 × 16 = 128
They match, so both answers are right
Dividing the top and bottom of 8/16 by 8 reduces it to 1/2, which is as far as it goes. Anything smaller than the GCF would leave the fraction reducible.
GCF of 8 and 16: FAQs
What is the GCF of 8 and 16?
The GCF of 8 and 16 is 8. It is the largest whole number that divides both of them exactly.
What are the common factors of 8 and 16?
The common factors of 8 and 16 are 1, 2, 4 and 8. The greatest of them is 8.
Is the GCF of 16 and 8 the same as the GCF of 8 and 16?
Yes. The order makes no difference. The greatest common factor of 16 and 8 is 8, exactly the same as the GCF of 8 and 16, 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 16 and 8.
What is the LCM of 8 and 16?
The LCM of 8 and 16 is 16. You can check it with GCF times LCM: 8 times 16 equals 128, which is the same as 8 times 16.
Are 8 and 16 coprime?
No. 8 and 16 share 8 as a common factor, so they are not coprime. Coprime numbers have a GCF of exactly 1.
How do you simplify 8/16?
Divide the top and the bottom by their GCF, which is 8. That gives 8 divided by 8 equals 1, and 16 divided by 8 equals 2, so 8/16 simplifies to 1/2.
Which method is quickest for 8 and 16?
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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