What is the Greatest Common Factor of 30120 and 30140?

Greatest common factor (GCF) of 30120 and 30140 is 20.

GCF(30120,30140) = 20

We will now calculate the prime factors of 30120 and 30140, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30120 and 30140.

How to find the GCF of 30120 and 30140?

We will first find the prime factorization of 30120 and 30140. After we will calculate the factors of 30120 and 30140 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 30140

Prime factors of 30140 are 2, 5, 11, 137. Prime factorization of 30140 in exponential form is:

30140 = 2² × 5¹ × 11¹ × 137¹

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 30140

List of positive integer factors of 30140 that divides 30120 without a remainder.

1, 2, 4, 5, 10, 11, 20, 22, 44, 55, 110, 137, 220, 274, 548, 685, 1370, 1507, 2740, 3014, 6028, 7535, 15070

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30120 and 30140. The biggest common factor number is the GCF number.
So the greatest common factor 30120 and 30140 is 20.

Also check out the Least Common Multiple of 30120 and 30140