What is the Greatest Common Factor of 30120 and 30128?

Greatest common factor (GCF) of 30120 and 30128 is 8.

GCF(30120,30128) = 8

We will now calculate the prime factors of 30120 and 30128, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30120 and 30128.

How to find the GCF of 30120 and 30128?

We will first find the prime factorization of 30120 and 30128. After we will calculate the factors of 30120 and 30128 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 30128

Prime factors of 30128 are 2, 7, 269. Prime factorization of 30128 in exponential form is:

30128 = 2⁴ × 7¹ × 269¹

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 30128

List of positive integer factors of 30128 that divides 30120 without a remainder.

1, 2, 4, 7, 8, 14, 16, 28, 56, 112, 269, 538, 1076, 1883, 2152, 3766, 4304, 7532, 15064

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30120 and 30128. The biggest common factor number is the GCF number.
So the greatest common factor 30120 and 30128 is 8.

Also check out the Least Common Multiple of 30120 and 30128