What is the Greatest Common Factor of 23200 and 23219?

Greatest common factor (GCF) of 23200 and 23219 is 1.

GCF(23200,23219) = 1

We will now calculate the prime factors of 23200 and 23219, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 23200 and 23219.

How to find the GCF of 23200 and 23219?

We will first find the prime factorization of 23200 and 23219. After we will calculate the factors of 23200 and 23219 and find the biggest common factor number .

Step-1: Prime Factorization of 23200

Prime factors of 23200 are 2, 5, 29. Prime factorization of 23200 in exponential form is:

23200 = 2⁵ × 5² × 29¹

Step-2: Prime Factorization of 23219

Prime factors of 23219 are 7, 31, 107. Prime factorization of 23219 in exponential form is:

23219 = 7¹ × 31¹ × 107¹

Step-3: Factors of 23200

List of positive integer factors of 23200 that divides 23200 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 25, 29, 32, 40, 50, 58, 80, 100, 116, 145, 160, 200, 232, 290, 400, 464, 580, 725, 800, 928, 1160, 1450, 2320, 2900, 4640, 5800, 11600

Step-4: Factors of 23219

List of positive integer factors of 23219 that divides 23200 without a remainder.

1, 7, 31, 107, 217, 749, 3317

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 23200 and 23219. The biggest common factor number is the GCF number.
So the greatest common factor 23200 and 23219 is 1.

Also check out the Least Common Multiple of 23200 and 23219