What is the Greatest Common Factor of 60 and 468?

Greatest common factor (GCF) of 60 and 468 is 12.

GCF(60,468) = 12

We will now calculate the prime factors of 60 and 468, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 60 and 468.

How to find the GCF of 60 and 468?

We will first find the prime factorization of 60 and 468. After we will calculate the factors of 60 and 468 and find the biggest common factor number .

Step-1: Prime Factorization of 60

Prime factors of 60 are 2, 3, 5. Prime factorization of 60 in exponential form is:

60 = 2² × 3¹ × 5¹

Step-2: Prime Factorization of 468

Prime factors of 468 are 2, 3, 13. Prime factorization of 468 in exponential form is:

468 = 2² × 3² × 13¹

Step-3: Factors of 60

List of positive integer factors of 60 that divides 60 without a remainder.

1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30

Step-4: Factors of 468

List of positive integer factors of 468 that divides 60 without a remainder.

1, 2, 3, 4, 6, 9, 12, 13, 18, 26, 36, 39, 52, 78, 117, 156, 234

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 60 and 468. The biggest common factor number is the GCF number.
So the greatest common factor 60 and 468 is 12.

Also check out the Least Common Multiple of 60 and 468