What is the Greatest Common Factor of 30 and 150?

Greatest common factor (GCF) of 30 and 150 is 30.

GCF(30,150) = 30

We will now calculate the prime factors of 30 and 150, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30 and 150.

How to find the GCF of 30 and 150?

We will first find the prime factorization of 30 and 150. After we will calculate the factors of 30 and 150 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 150

Prime factors of 150 are 2, 3, 5. Prime factorization of 150 in exponential form is:

150 = 2¹ × 3¹ × 5²

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 150

List of positive integer factors of 150 that divides 30 without a remainder.

1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30 and 150. The biggest common factor number is the GCF number.
So the greatest common factor 30 and 150 is 30.

Also check out the Least Common Multiple of 30 and 150