What is the Greatest Common Factor of 72225 and 72240?

Greatest common factor (GCF) of 72225 and 72240 is 15.

GCF(72225,72240) = 15

We will now calculate the prime factors of 72225 and 72240, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 72225 and 72240.

How to find the GCF of 72225 and 72240?

We will first find the prime factorization of 72225 and 72240. After we will calculate the factors of 72225 and 72240 and find the biggest common factor number .

Step-1: Prime Factorization of 72225

Prime factors of 72225 are 3, 5, 107. Prime factorization of 72225 in exponential form is:

72225 = 3³ × 5² × 107¹

Step-2: Prime Factorization of 72240

Prime factors of 72240 are 2, 3, 5, 7, 43. Prime factorization of 72240 in exponential form is:

72240 = 2⁴ × 3¹ × 5¹ × 7¹ × 43¹

Step-3: Factors of 72225

List of positive integer factors of 72225 that divides 72225 without a remainder.

1, 3, 5, 9, 15, 25, 27, 45, 75, 107, 135, 225, 321, 535, 675, 963, 1605, 2675, 2889, 4815, 8025, 14445, 24075

Step-4: Factors of 72240

List of positive integer factors of 72240 that divides 72225 without a remainder.

1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 16, 20, 21, 24, 28, 30, 35, 40, 42, 43, 48, 56, 60, 70, 80, 84, 86, 105, 112, 120, 129, 140, 168, 172, 210, 215, 240, 258, 280, 301, 336, 344, 420, 430, 516, 560, 602, 645, 688, 840, 860, 903, 1032, 1204, 1290, 1505, 1680, 1720, 1806, 2064, 2408, 2580, 3010, 3440, 3612, 4515, 4816, 5160, 6020, 7224, 9030, 10320, 12040, 14448, 18060, 24080, 36120

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 72225 and 72240. The biggest common factor number is the GCF number.
So the greatest common factor 72225 and 72240 is 15.

Also check out the Least Common Multiple of 72225 and 72240