What is the Greatest Common Factor of 2280 and 2300?

Greatest common factor (GCF) of 2280 and 2300 is 20.

GCF(2280,2300) = 20

We will now calculate the prime factors of 2280 and 2300, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 2280 and 2300.

How to find the GCF of 2280 and 2300?

We will first find the prime factorization of 2280 and 2300. After we will calculate the factors of 2280 and 2300 and find the biggest common factor number .

Step-1: Prime Factorization of 2280

Prime factors of 2280 are 2, 3, 5, 19. Prime factorization of 2280 in exponential form is:

2280 = 2³ × 3¹ × 5¹ × 19¹

Step-2: Prime Factorization of 2300

Prime factors of 2300 are 2, 5, 23. Prime factorization of 2300 in exponential form is:

2300 = 2² × 5² × 23¹

Step-3: Factors of 2280

List of positive integer factors of 2280 that divides 2280 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 19, 20, 24, 30, 38, 40, 57, 60, 76, 95, 114, 120, 152, 190, 228, 285, 380, 456, 570, 760, 1140

Step-4: Factors of 2300

List of positive integer factors of 2300 that divides 2280 without a remainder.

1, 2, 4, 5, 10, 20, 23, 25, 46, 50, 92, 100, 115, 230, 460, 575, 1150

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 2280 and 2300. The biggest common factor number is the GCF number.
So the greatest common factor 2280 and 2300 is 20.

Also check out the Least Common Multiple of 2280 and 2300