What is the Greatest Common Factor of 102 and 108?

Greatest common factor (GCF) of 102 and 108 is 6.

GCF(102,108) = 6

We will now calculate the prime factors of 102 and 108, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 102 and 108.

How to find the GCF of 102 and 108?

We will first find the prime factorization of 102 and 108. After we will calculate the factors of 102 and 108 and find the biggest common factor number .

Step-1: Prime Factorization of 102

Prime factors of 102 are 2, 3, 17. Prime factorization of 102 in exponential form is:

102 = 2¹ × 3¹ × 17¹

Step-2: Prime Factorization of 108

Prime factors of 108 are 2, 3. Prime factorization of 108 in exponential form is:

108 = 2² × 3³

Step-3: Factors of 102

List of positive integer factors of 102 that divides 102 without a remainder.

1, 2, 3, 6, 17, 34, 51

Step-4: Factors of 108

List of positive integer factors of 108 that divides 102 without a remainder.

1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 102 and 108. The biggest common factor number is the GCF number.
So the greatest common factor 102 and 108 is 6.

Also check out the Least Common Multiple of 102 and 108