What is the Greatest Common Factor of 30108 and 30120?

Greatest common factor (GCF) of 30108 and 30120 is 12.

GCF(30108,30120) = 12

We will now calculate the prime factors of 30108 and 30120, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30108 and 30120.

How to find the GCF of 30108 and 30120?

We will first find the prime factorization of 30108 and 30120. After we will calculate the factors of 30108 and 30120 and find the biggest common factor number .

Step-1: Prime Factorization of 30108

Prime factors of 30108 are 2, 3, 13, 193. Prime factorization of 30108 in exponential form is:

30108 = 2² × 3¹ × 13¹ × 193¹

Step-2: Prime Factorization of 30120

Prime factors of 30120 are 2, 3, 5, 251. Prime factorization of 30120 in exponential form is:

30120 = 2³ × 3¹ × 5¹ × 251¹

Step-3: Factors of 30108

List of positive integer factors of 30108 that divides 30108 without a remainder.

1, 2, 3, 4, 6, 12, 13, 26, 39, 52, 78, 156, 193, 386, 579, 772, 1158, 2316, 2509, 5018, 7527, 10036, 15054

Step-4: Factors of 30120

List of positive integer factors of 30120 that divides 30108 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120, 251, 502, 753, 1004, 1255, 1506, 2008, 2510, 3012, 3765, 5020, 6024, 7530, 10040, 15060

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30108 and 30120. The biggest common factor number is the GCF number.
So the greatest common factor 30108 and 30120 is 12.

Also check out the Least Common Multiple of 30108 and 30120