What is the Greatest Common Factor of 30120 and 30132?

Greatest common factor (GCF) of 30120 and 30132 is 12.

GCF(30120,30132) = 12

We will now calculate the prime factors of 30120 and 30132, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30120 and 30132.

How to find the GCF of 30120 and 30132?

We will first find the prime factorization of 30120 and 30132. After we will calculate the factors of 30120 and 30132 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 30132

Prime factors of 30132 are 2, 3, 31. Prime factorization of 30132 in exponential form is:

30132 = 2² × 3⁵ × 31¹

Step-3: Factors of 30120

List of positive integer factors of 30120 that divides 30120 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

Step-4: Factors of 30132

List of positive integer factors of 30132 that divides 30120 without a remainder.

1, 2, 3, 4, 6, 9, 12, 18, 27, 31, 36, 54, 62, 81, 93, 108, 124, 162, 186, 243, 279, 324, 372, 486, 558, 837, 972, 1116, 1674, 2511, 3348, 5022, 7533, 10044, 15066

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30120 and 30132. The biggest common factor number is the GCF number.
So the greatest common factor 30120 and 30132 is 12.

Also check out the Least Common Multiple of 30120 and 30132