What is the Greatest Common Factor of 2280 and 2299?

Greatest common factor (GCF) of 2280 and 2299 is 19.

GCF(2280,2299) = 19

We will now calculate the prime factors of 2280 and 2299, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 2280 and 2299.

How to find the GCF of 2280 and 2299?

We will first find the prime factorization of 2280 and 2299. After we will calculate the factors of 2280 and 2299 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 2299

Prime factors of 2299 are 11, 19. Prime factorization of 2299 in exponential form is:

2299 = 11² × 19¹

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 2299

List of positive integer factors of 2299 that divides 2280 without a remainder.

1, 11, 19, 121, 209

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 2280 and 2299. The biggest common factor number is the GCF number.
So the greatest common factor 2280 and 2299 is 19.

Also check out the Least Common Multiple of 2280 and 2299