What is the Greatest Common Factor of 60 and 105?

Greatest common factor (GCF) of 60 and 105 is 15.

GCF(60,105) = 15

We will now calculate the prime factors of 60 and 105, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 60 and 105.

How to find the GCF of 60 and 105?

We will first find the prime factorization of 60 and 105. After we will calculate the factors of 60 and 105 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 105

Prime factors of 105 are 3, 5, 7. Prime factorization of 105 in exponential form is:

105 = 3¹ × 5¹ × 7¹

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 105

List of positive integer factors of 105 that divides 60 without a remainder.

1, 3, 5, 7, 15, 21, 35

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 60 and 105. The biggest common factor number is the GCF number.
So the greatest common factor 60 and 105 is 15.

Also check out the Least Common Multiple of 60 and 105