What is the Greatest Common Factor of 8100 and 8120?

Greatest common factor (GCF) of 8100 and 8120 is 20.

GCF(8100,8120) = 20

We will now calculate the prime factors of 8100 and 8120, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 8100 and 8120.

How to find the GCF of 8100 and 8120?

We will first find the prime factorization of 8100 and 8120. After we will calculate the factors of 8100 and 8120 and find the biggest common factor number .

Step-1: Prime Factorization of 8100

Prime factors of 8100 are 2, 3, 5. Prime factorization of 8100 in exponential form is:

8100 = 2² × 3⁴ × 5²

Step-2: Prime Factorization of 8120

Prime factors of 8120 are 2, 5, 7, 29. Prime factorization of 8120 in exponential form is:

8120 = 2³ × 5¹ × 7¹ × 29¹

Step-3: Factors of 8100

List of positive integer factors of 8100 that divides 8100 without a remainder.

1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 25, 27, 30, 36, 45, 50, 54, 60, 75, 81, 90, 100, 108, 135, 150, 162, 180, 225, 270, 300, 324, 405, 450, 540, 675, 810, 900, 1350, 1620, 2025, 2700, 4050

Step-4: Factors of 8120

List of positive integer factors of 8120 that divides 8100 without a remainder.

1, 2, 4, 5, 7, 8, 10, 14, 20, 28, 29, 35, 40, 56, 58, 70, 116, 140, 145, 203, 232, 280, 290, 406, 580, 812, 1015, 1160, 1624, 2030, 4060

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 8100 and 8120. The biggest common factor number is the GCF number.
So the greatest common factor 8100 and 8120 is 20.

Also check out the Least Common Multiple of 8100 and 8120