Mathematics · Greatest common factor
GCF of 20 and 30
The greatest common factor of 20 and 30 is 10. It is the largest whole number that divides both 20 and 30 with no remainder.
You will also see it written as the highest common factor (HCF) or the greatest common divisor (GCD) of 20 and 30. All three names mean the same thing.
Greatest common factor
10
GCF, GCD or HCF of 20 and 30
Least common multiple
60
LCM of 20 and 30
20/30 simplified
2/3
both divided by 10
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 30
Factors of 20: 1, 2, 4, 5, 10, 20
Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30
Common factors: 1, 2, 5, 10
Greatest of those = 10
The common factors of 20 and 30 are 1, 2, 5 and 10, and that is the complete list. The largest one, 10, is the GCF.
Prime factorization method
20 = 22 × 5 (2 × 2 × 5)
30 = 2 × 3 × 5 (2 × 3 × 5)
Shared primes at their lowest power: 2 × 5
GCF = 10
Take every prime that appears in both lists, each at the lower of its two powers, and multiply them: 2 × 5 gives 10.
Euclid's algorithm, step by step
30 ÷ 20 = 1 remainder 10
20 ÷ 10 = 2 remainder 0
Last non-zero remainder = 10, so the GCF is 10
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 30.
LCM of 20 and 30, and the fraction 20/30
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 = 10 × 60 = 600
20 × 30 = 600
They match, so both answers are right
Dividing the top and bottom of 20/30 by 10 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
Twenty and thirty minute slots both fit into an hour, and both are multiples of their GCF, 10.
GCF of 20 and 30: FAQs
What is the GCF of 20 and 30?
The GCF of 20 and 30 is 10. It is the largest whole number that divides both of them exactly.
What are the common factors of 20 and 30?
The common factors of 20 and 30 are 1, 2, 5 and 10. The greatest of them is 10.
Is the GCF of 30 and 20 the same as the GCF of 20 and 30?
Yes. The order makes no difference. The greatest common factor of 30 and 20 is 10, exactly the same as the GCF of 20 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 20.
What is the LCM of 20 and 30?
The LCM of 20 and 30 is 60. You can check it with GCF times LCM: 10 times 60 equals 600, which is the same as 20 times 30.
Are 20 and 30 coprime?
No. 20 and 30 share 10 as a common factor, so they are not coprime. Coprime numbers have a GCF of exactly 1.
How do you simplify 20/30?
Divide the top and the bottom by their GCF, which is 10. That gives 20 divided by 10 equals 2, and 30 divided by 10 equals 3, so 20/30 simplifies to 2/3.
Which method is quickest for 20 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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