What is the Greatest Common Factor of 30100 and 30120?

Greatest common factor (GCF) of 30100 and 30120 is 20.

GCF(30100,30120) = 20

We will now calculate the prime factors of 30100 and 30120, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30100 and 30120.

How to find the GCF of 30100 and 30120?

We will first find the prime factorization of 30100 and 30120. After we will calculate the factors of 30100 and 30120 and find the biggest common factor number .

Step-1: Prime Factorization of 30100

Prime factors of 30100 are 2, 5, 7, 43. Prime factorization of 30100 in exponential form is:

30100 = 2² × 5² × 7¹ × 43¹

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 30100

List of positive integer factors of 30100 that divides 30100 without a remainder.

1, 2, 4, 5, 7, 10, 14, 20, 25, 28, 35, 43, 50, 70, 86, 100, 140, 172, 175, 215, 301, 350, 430, 602, 700, 860, 1075, 1204, 1505, 2150, 3010, 4300, 6020, 7525, 15050

Step-4: Factors of 30120

List of positive integer factors of 30120 that divides 30100 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 30100 and 30120. The biggest common factor number is the GCF number.
So the greatest common factor 30100 and 30120 is 20.

Also check out the Least Common Multiple of 30100 and 30120