Mathematics · Greatest common factor
GCF of 24 and 40
The greatest common factor of 24 and 40 is 8. It is the largest whole number that divides both 24 and 40 with no remainder.
You will also see it written as the highest common factor (HCF) or the greatest common divisor (GCD) of 24 and 40. All three names mean the same thing.
Greatest common factor
8
GCF, GCD or HCF of 24 and 40
Least common multiple
120
LCM of 24 and 40
24/40 simplified
3/5
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 24 and 40
Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
Factors of 40: 1, 2, 4, 5, 8, 10, 20, 40
Common factors: 1, 2, 4, 8
Greatest of those = 8
The common factors of 24 and 40 are 1, 2, 4 and 8, and that is the complete list. The largest one, 8, is the GCF.
Prime factorization method
24 = 23 × 3 (2 × 2 × 2 × 3)
40 = 23 × 5 (2 × 2 × 2 × 5)
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
40 ÷ 24 = 1 remainder 16
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 3 steps for 24 and 40.
LCM of 24 and 40, and the fraction 24/40
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 × 120 = 960
24 × 40 = 960
They match, so both answers are right
Dividing the top and bottom of 24/40 by 8 reduces it to 3/5, which is as far as it goes. Anything smaller than the GCF would leave the fraction reducible.
Where these two numbers turn up
Twenty four and forty hour weeks both divide into 8 hour shifts, their greatest common factor.
GCF of 24 and 40: FAQs
What is the GCF of 24 and 40?
The GCF of 24 and 40 is 8. It is the largest whole number that divides both of them exactly.
What are the common factors of 24 and 40?
The common factors of 24 and 40 are 1, 2, 4 and 8. The greatest of them is 8.
Is the GCF of 40 and 24 the same as the GCF of 24 and 40?
Yes. The order makes no difference. The greatest common factor of 40 and 24 is 8, exactly the same as the GCF of 24 and 40, 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 40 and 24.
What is the LCM of 24 and 40?
The LCM of 24 and 40 is 120. You can check it with GCF times LCM: 8 times 120 equals 960, which is the same as 24 times 40.
Are 24 and 40 coprime?
No. 24 and 40 share 8 as a common factor, so they are not coprime. Coprime numbers have a GCF of exactly 1.
How do you simplify 24/40?
Divide the top and the bottom by their GCF, which is 8. That gives 24 divided by 8 equals 3, and 40 divided by 8 equals 5, so 24/40 simplifies to 3/5.
Which method is quickest for 24 and 40?
Euclid's algorithm, because it reaches the answer in 3 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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