What is the Greatest Common Factor of 30 and 18?

Greatest common factor (GCF) of 30 and 18 is 6.

GCF(30,18) = 6

We will now calculate the prime factors of 30 and 18, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30 and 18.

How to find the GCF of 30 and 18?

We will first find the prime factorization of 30 and 18. After we will calculate the factors of 30 and 18 and find the biggest common factor number .

Step-1: Prime Factorization of 30

Prime factors of 30 are 2, 3, 5. Prime factorization of 30 in exponential form is:

30 = 2¹ × 3¹ × 5¹

Step-2: Prime Factorization of 18

Prime factors of 18 are 2, 3. Prime factorization of 18 in exponential form is:

18 = 2¹ × 3²

Step-3: Factors of 30

List of positive integer factors of 30 that divides 30 without a remainder.

1, 2, 3, 5, 6, 10, 15

Step-4: Factors of 18

List of positive integer factors of 18 that divides 30 without a remainder.

1, 2, 3, 6, 9

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30 and 18. The biggest common factor number is the GCF number.
So the greatest common factor 30 and 18 is 6.

Also check out the Least Common Multiple of 30 and 18