What is the Greatest Common Factor of 24288 and 24300?

Greatest common factor (GCF) of 24288 and 24300 is 12.

GCF(24288,24300) = 12

We will now calculate the prime factors of 24288 and 24300, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 24288 and 24300.

How to find the GCF of 24288 and 24300?

We will first find the prime factorization of 24288 and 24300. After we will calculate the factors of 24288 and 24300 and find the biggest common factor number .

Step-1: Prime Factorization of 24288

Prime factors of 24288 are 2, 3, 11, 23. Prime factorization of 24288 in exponential form is:

24288 = 2⁵ × 3¹ × 11¹ × 23¹

Step-2: 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-3: Factors of 24288

List of positive integer factors of 24288 that divides 24288 without a remainder.

1, 2, 3, 4, 6, 8, 11, 12, 16, 22, 23, 24, 32, 33, 44, 46, 48, 66, 69, 88, 92, 96, 132, 138, 176, 184, 253, 264, 276, 352, 368, 506, 528, 552, 736, 759, 1012, 1056, 1104, 1518, 2024, 2208, 3036, 4048, 6072, 8096, 12144

Step-4: Factors of 24300

List of positive integer factors of 24300 that divides 24288 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 24288 and 24300. The biggest common factor number is the GCF number.
So the greatest common factor 24288 and 24300 is 12.

Also check out the Least Common Multiple of 24288 and 24300