What is the Greatest Common Factor of 30 and 450?

Greatest common factor (GCF) of 30 and 450 is 30.

GCF(30,450) = 30

We will now calculate the prime factors of 30 and 450, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30 and 450.

How to find the GCF of 30 and 450?

We will first find the prime factorization of 30 and 450. After we will calculate the factors of 30 and 450 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 450

Prime factors of 450 are 2, 3, 5. Prime factorization of 450 in exponential form is:

450 = 2¹ × 3² × 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 450

List of positive integer factors of 450 that divides 30 without a remainder.

1, 2, 3, 5, 6, 9, 10, 15, 18, 25, 30, 45, 50, 75, 90, 150, 225

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30 and 450. The biggest common factor number is the GCF number.
So the greatest common factor 30 and 450 is 30.

Also check out the Least Common Multiple of 30 and 450