Mathematics · Greatest common factor
GCF of 30 and 45
The greatest common factor of 30 and 45 is 15. It is the largest whole number that divides both 30 and 45 with no remainder.
You will also see it written as the highest common factor (HCF) or the greatest common divisor (GCD) of 30 and 45. All three names mean the same thing.
Greatest common factor
15
GCF, GCD or HCF of 30 and 45
Least common multiple
90
LCM of 30 and 45
30/45 simplified
2/3
both divided by 15
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 30 and 45
Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30
Factors of 45: 1, 3, 5, 9, 15, 45
Common factors: 1, 3, 5, 15
Greatest of those = 15
The common factors of 30 and 45 are 1, 3, 5 and 15, and that is the complete list. The largest one, 15, is the GCF.
Prime factorization method
30 = 2 × 3 × 5 (2 × 3 × 5)
45 = 32 × 5 (3 × 3 × 5)
Shared primes at their lowest power: 3 × 5
GCF = 15
Take every prime that appears in both lists, each at the lower of its two powers, and multiply them: 3 × 5 gives 15.
Euclid's algorithm, step by step
45 ÷ 30 = 1 remainder 15
30 ÷ 15 = 2 remainder 0
Last non-zero remainder = 15, so the GCF is 15
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 30 and 45.
LCM of 30 and 45, and the fraction 30/45
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 = 15 × 90 = 1,350
30 × 45 = 1,350
They match, so both answers are right
Dividing the top and bottom of 30/45 by 15 reduces it to 2/3, which is as far as it goes. Anything smaller than the GCF would leave the fraction reducible.
GCF of 30 and 45: FAQs
What is the GCF of 30 and 45?
The GCF of 30 and 45 is 15. It is the largest whole number that divides both of them exactly.
What are the common factors of 30 and 45?
The common factors of 30 and 45 are 1, 3, 5 and 15. The greatest of them is 15.
Is the GCF of 45 and 30 the same as the GCF of 30 and 45?
Yes. The order makes no difference. The greatest common factor of 45 and 30 is 15, exactly the same as the GCF of 30 and 45, 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 45 and 30.
What is the LCM of 30 and 45?
The LCM of 30 and 45 is 90. You can check it with GCF times LCM: 15 times 90 equals 1,350, which is the same as 30 times 45.
Are 30 and 45 coprime?
No. 30 and 45 share 15 as a common factor, so they are not coprime. Coprime numbers have a GCF of exactly 1.
How do you simplify 30/45?
Divide the top and the bottom by their GCF, which is 15. That gives 30 divided by 15 equals 2, and 45 divided by 15 equals 3, so 30/45 simplifies to 2/3.
Which method is quickest for 30 and 45?
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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