Mathematics · Greatest common factor
GCF of 40 and 48
The greatest common factor of 40 and 48 is 8. It is the largest whole number that divides both 40 and 48 with no remainder.
You will also see it written as the highest common factor (HCF) or the greatest common divisor (GCD) of 40 and 48. All three names mean the same thing.
Greatest common factor
8
GCF, GCD or HCF of 40 and 48
Least common multiple
240
LCM of 40 and 48
40/48 simplified
5/6
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 40 and 48
Factors of 40: 1, 2, 4, 5, 8, 10, 20, 40
Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
Common factors: 1, 2, 4, 8
Greatest of those = 8
The common factors of 40 and 48 are 1, 2, 4 and 8, and that is the complete list. The largest one, 8, is the GCF.
Prime factorization method
40 = 23 × 5 (2 × 2 × 2 × 5)
48 = 24 × 3 (2 × 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
48 ÷ 40 = 1 remainder 8
40 ÷ 8 = 5 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 40 and 48.
LCM of 40 and 48, and the fraction 40/48
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 × 240 = 1,920
40 × 48 = 1,920
They match, so both answers are right
Dividing the top and bottom of 40/48 by 8 reduces it to 5/6, which is as far as it goes. Anything smaller than the GCF would leave the fraction reducible.
GCF of 40 and 48: FAQs
What is the GCF of 40 and 48?
The GCF of 40 and 48 is 8. It is the largest whole number that divides both of them exactly.
What are the common factors of 40 and 48?
The common factors of 40 and 48 are 1, 2, 4 and 8. The greatest of them is 8.
Is the GCF of 48 and 40 the same as the GCF of 40 and 48?
Yes. The order makes no difference. The greatest common factor of 48 and 40 is 8, exactly the same as the GCF of 40 and 48, 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 48 and 40.
What is the LCM of 40 and 48?
The LCM of 40 and 48 is 240. You can check it with GCF times LCM: 8 times 240 equals 1,920, which is the same as 40 times 48.
Are 40 and 48 coprime?
No. 40 and 48 share 8 as a common factor, so they are not coprime. Coprime numbers have a GCF of exactly 1.
How do you simplify 40/48?
Divide the top and the bottom by their GCF, which is 8. That gives 40 divided by 8 equals 5, and 48 divided by 8 equals 6, so 40/48 simplifies to 5/6.
Which method is quickest for 40 and 48?
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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