Mathematics · Greatest common factor
GCF of 16 and 24
The greatest common factor of 16 and 24 is 8. It is the largest whole number that divides both 16 and 24 with no remainder.
You will also see it written as the highest common factor (HCF) or the greatest common divisor (GCD) of 16 and 24. All three names mean the same thing.
Greatest common factor
8
GCF, GCD or HCF of 16 and 24
Least common multiple
48
LCM of 16 and 24
16/24 simplified
2/3
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 16 and 24
Factors of 16: 1, 2, 4, 8, 16
Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
Common factors: 1, 2, 4, 8
Greatest of those = 8
The common factors of 16 and 24 are 1, 2, 4 and 8, and that is the complete list. The largest one, 8, is the GCF.
Prime factorization method
16 = 24 (2 × 2 × 2 × 2)
24 = 23 × 3 (2 × 2 × 2 × 3)
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
24 ÷ 16 = 1 remainder 8
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 2 steps for 16 and 24.
LCM of 16 and 24, and the fraction 16/24
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 × 48 = 384
16 × 24 = 384
They match, so both answers are right
Dividing the top and bottom of 16/24 by 8 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
Stud spacings of 16 and 24 inches line up again every 48 inches, which is their least common multiple.
GCF of 16 and 24: FAQs
What is the GCF of 16 and 24?
The GCF of 16 and 24 is 8. It is the largest whole number that divides both of them exactly.
What are the common factors of 16 and 24?
The common factors of 16 and 24 are 1, 2, 4 and 8. The greatest of them is 8.
Is the GCF of 24 and 16 the same as the GCF of 16 and 24?
Yes. The order makes no difference. The greatest common factor of 24 and 16 is 8, exactly the same as the GCF of 16 and 24, 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 24 and 16.
What is the LCM of 16 and 24?
The LCM of 16 and 24 is 48. You can check it with GCF times LCM: 8 times 48 equals 384, which is the same as 16 times 24.
Are 16 and 24 coprime?
No. 16 and 24 share 8 as a common factor, so they are not coprime. Coprime numbers have a GCF of exactly 1.
How do you simplify 16/24?
Divide the top and the bottom by their GCF, which is 8. That gives 16 divided by 8 equals 2, and 24 divided by 8 equals 3, so 16/24 simplifies to 2/3.
Which method is quickest for 16 and 24?
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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