What is the Greatest Common Factor of 102 and 120?

Greatest common factor (GCF) of 102 and 120 is 6.

GCF(102,120) = 6

We will now calculate the prime factors of 102 and 120, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 102 and 120.

How to find the GCF of 102 and 120?

We will first find the prime factorization of 102 and 120. After we will calculate the factors of 102 and 120 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 120

Prime factors of 120 are 2, 3, 5. Prime factorization of 120 in exponential form is:

120 = 2³ × 3¹ × 5¹

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 120

List of positive integer factors of 120 that divides 102 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 102 and 120. The biggest common factor number is the GCF number.
So the greatest common factor 102 and 120 is 6.

Also check out the Least Common Multiple of 102 and 120