What is the Greatest Common Factor of 30120 and 30130?

Greatest common factor (GCF) of 30120 and 30130 is 10.

GCF(30120,30130) = 10

We will now calculate the prime factors of 30120 and 30130, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30120 and 30130.

How to find the GCF of 30120 and 30130?

We will first find the prime factorization of 30120 and 30130. After we will calculate the factors of 30120 and 30130 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 30130

Prime factors of 30130 are 2, 5, 23, 131. Prime factorization of 30130 in exponential form is:

30130 = 2¹ × 5¹ × 23¹ × 131¹

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 30130

List of positive integer factors of 30130 that divides 30120 without a remainder.

1, 2, 5, 10, 23, 46, 115, 131, 230, 262, 655, 1310, 3013, 6026, 15065

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30120 and 30130. The biggest common factor number is the GCF number.
So the greatest common factor 30120 and 30130 is 10.

Also check out the Least Common Multiple of 30120 and 30130