What is the Greatest Common Factor of 24300 and 24320?

Greatest common factor (GCF) of 24300 and 24320 is 20.

GCF(24300,24320) = 20

We will now calculate the prime factors of 24300 and 24320, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 24300 and 24320.

How to find the GCF of 24300 and 24320?

We will first find the prime factorization of 24300 and 24320. After we will calculate the factors of 24300 and 24320 and find the biggest common factor number .

Step-1: Prime Factorization of 24300

Prime factors of 24300 are 2, 3, 5. Prime factorization of 24300 in exponential form is:

24300 = 2² × 3⁵ × 5²

Step-2: Prime Factorization of 24320

Prime factors of 24320 are 2, 5, 19. Prime factorization of 24320 in exponential form is:

24320 = 2⁸ × 5¹ × 19¹

Step-3: Factors of 24300

List of positive integer factors of 24300 that divides 24300 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, 243, 270, 300, 324, 405, 450, 486, 540, 675, 810, 900, 972, 1215, 1350, 1620, 2025, 2430, 2700, 4050, 4860, 6075, 8100, 12150

Step-4: Factors of 24320

List of positive integer factors of 24320 that divides 24300 without a remainder.

1, 2, 4, 5, 8, 10, 16, 19, 20, 32, 38, 40, 64, 76, 80, 95, 128, 152, 160, 190, 256, 304, 320, 380, 608, 640, 760, 1216, 1280, 1520, 2432, 3040, 4864, 6080, 12160

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 24300 and 24320. The biggest common factor number is the GCF number.
So the greatest common factor 24300 and 24320 is 20.

Also check out the Least Common Multiple of 24300 and 24320