Mathematics · Greatest common factor
GCF of 20 and 24
The greatest common factor of 20 and 24 is 4. It is the largest whole number that divides both 20 and 24 with no remainder.
You will also see it written as the highest common factor (HCF) or the greatest common divisor (GCD) of 20 and 24. All three names mean the same thing.
Greatest common factor
4
GCF, GCD or HCF of 20 and 24
Least common multiple
120
LCM of 20 and 24
20/24 simplified
5/6
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 20 and 24
Factors of 20: 1, 2, 4, 5, 10, 20
Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
Common factors: 1, 2, 4
Greatest of those = 4
The common factors of 20 and 24 are 1, 2 and 4, and that is the complete list. The largest one, 4, is the GCF.
Prime factorization method
20 = 22 × 5 (2 × 2 × 5)
24 = 23 × 3 (2 × 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
24 ÷ 20 = 1 remainder 4
20 ÷ 4 = 5 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 20 and 24.
LCM of 20 and 24, and the fraction 20/24
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 = 4 × 120 = 480
20 × 24 = 480
They match, so both answers are right
Dividing the top and bottom of 20/24 by 4 reduces it to 5/6, which is as far as it goes. Anything smaller than the GCF would leave the fraction reducible.
GCF of 20 and 24: FAQs
What is the GCF of 20 and 24?
The GCF of 20 and 24 is 4. It is the largest whole number that divides both of them exactly.
What are the common factors of 20 and 24?
The common factors of 20 and 24 are 1, 2 and 4. The greatest of them is 4.
Is the GCF of 24 and 20 the same as the GCF of 20 and 24?
Yes. The order makes no difference. The greatest common factor of 24 and 20 is 4, exactly the same as the GCF of 20 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 20.
What is the LCM of 20 and 24?
The LCM of 20 and 24 is 120. You can check it with GCF times LCM: 4 times 120 equals 480, which is the same as 20 times 24.
Are 20 and 24 coprime?
No. 20 and 24 share 4 as a common factor, so they are not coprime. Coprime numbers have a GCF of exactly 1.
How do you simplify 20/24?
Divide the top and the bottom by their GCF, which is 4. That gives 20 divided by 4 equals 5, and 24 divided by 4 equals 6, so 20/24 simplifies to 5/6.
Which method is quickest for 20 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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