What is the Greatest Common Factor of 30120 and 30135?

Greatest common factor (GCF) of 30120 and 30135 is 15.

GCF(30120,30135) = 15

We will now calculate the prime factors of 30120 and 30135, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30120 and 30135.

How to find the GCF of 30120 and 30135?

We will first find the prime factorization of 30120 and 30135. After we will calculate the factors of 30120 and 30135 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 30135

Prime factors of 30135 are 3, 5, 7, 41. Prime factorization of 30135 in exponential form is:

30135 = 3¹ × 5¹ × 7² × 41¹

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 30135

List of positive integer factors of 30135 that divides 30120 without a remainder.

1, 3, 5, 7, 15, 21, 35, 41, 49, 105, 123, 147, 205, 245, 287, 615, 735, 861, 1435, 2009, 4305, 6027, 10045

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30120 and 30135. The biggest common factor number is the GCF number.
So the greatest common factor 30120 and 30135 is 15.

Also check out the Least Common Multiple of 30120 and 30135