Mathematics · Greatest common factor
GCF of 24 and 30
The greatest common factor of 24 and 30 is 6. It is the largest whole number that divides both 24 and 30 with no remainder.
You will also see it written as the highest common factor (HCF) or the greatest common divisor (GCD) of 24 and 30. All three names mean the same thing.
Greatest common factor
6
GCF, GCD or HCF of 24 and 30
Least common multiple
120
LCM of 24 and 30
24/30 simplified
4/5
both divided by 6
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 24 and 30
Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30
Common factors: 1, 2, 3, 6
Greatest of those = 6
The common factors of 24 and 30 are 1, 2, 3 and 6, and that is the complete list. The largest one, 6, is the GCF.
Prime factorization method
24 = 23 × 3 (2 × 2 × 2 × 3)
30 = 2 × 3 × 5 (2 × 3 × 5)
Shared primes at their lowest power: 2 × 3
GCF = 6
Take every prime that appears in both lists, each at the lower of its two powers, and multiply them: 2 × 3 gives 6.
Euclid's algorithm, step by step
30 ÷ 24 = 1 remainder 6
24 ÷ 6 = 4 remainder 0
Last non-zero remainder = 6, so the GCF is 6
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 24 and 30.
LCM of 24 and 30, and the fraction 24/30
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 = 6 × 120 = 720
24 × 30 = 720
They match, so both answers are right
Dividing the top and bottom of 24/30 by 6 reduces it to 4/5, which is as far as it goes. Anything smaller than the GCF would leave the fraction reducible.
GCF of 24 and 30: FAQs
What is the GCF of 24 and 30?
The GCF of 24 and 30 is 6. It is the largest whole number that divides both of them exactly.
What are the common factors of 24 and 30?
The common factors of 24 and 30 are 1, 2, 3 and 6. The greatest of them is 6.
Is the GCF of 30 and 24 the same as the GCF of 24 and 30?
Yes. The order makes no difference. The greatest common factor of 30 and 24 is 6, exactly the same as the GCF of 24 and 30, 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 30 and 24.
What is the LCM of 24 and 30?
The LCM of 24 and 30 is 120. You can check it with GCF times LCM: 6 times 120 equals 720, which is the same as 24 times 30.
Are 24 and 30 coprime?
No. 24 and 30 share 6 as a common factor, so they are not coprime. Coprime numbers have a GCF of exactly 1.
How do you simplify 24/30?
Divide the top and the bottom by their GCF, which is 6. That gives 24 divided by 6 equals 4, and 30 divided by 6 equals 5, so 24/30 simplifies to 4/5.
Which method is quickest for 24 and 30?
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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