What is the Greatest Common Factor of 72900 and 72912?

Greatest common factor (GCF) of 72900 and 72912 is 12.

GCF(72900,72912) = 12

We will now calculate the prime factors of 72900 and 72912, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 72900 and 72912.

How to find the GCF of 72900 and 72912?

We will first find the prime factorization of 72900 and 72912. After we will calculate the factors of 72900 and 72912 and find the biggest common factor number .

Step-1: Prime Factorization of 72900

Prime factors of 72900 are 2, 3, 5. Prime factorization of 72900 in exponential form is:

72900 = 2² × 3⁶ × 5²

Step-2: Prime Factorization of 72912

Prime factors of 72912 are 2, 3, 7, 31. Prime factorization of 72912 in exponential form is:

72912 = 2⁴ × 3¹ × 7² × 31¹

Step-3: Factors of 72900

List of positive integer factors of 72900 that divides 72900 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, 729, 810, 900, 972, 1215, 1350, 1458, 1620, 2025, 2430, 2700, 2916, 3645, 4050, 4860, 6075, 7290, 8100, 12150, 14580, 18225, 24300, 36450

Step-4: Factors of 72912

List of positive integer factors of 72912 that divides 72900 without a remainder.

1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 31, 42, 48, 49, 56, 62, 84, 93, 98, 112, 124, 147, 168, 186, 196, 217, 248, 294, 336, 372, 392, 434, 496, 588, 651, 744, 784, 868, 1176, 1302, 1488, 1519, 1736, 2352, 2604, 3038, 3472, 4557, 5208, 6076, 9114, 10416, 12152, 18228, 24304, 36456

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 72900 and 72912. The biggest common factor number is the GCF number.
So the greatest common factor 72900 and 72912 is 12.

Also check out the Least Common Multiple of 72900 and 72912