What is the Greatest Common Factor of 72135 and 72144?

Greatest common factor (GCF) of 72135 and 72144 is 9.

GCF(72135,72144) = 9

We will now calculate the prime factors of 72135 and 72144, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 72135 and 72144.

How to find the GCF of 72135 and 72144?

We will first find the prime factorization of 72135 and 72144. After we will calculate the factors of 72135 and 72144 and find the biggest common factor number .

Step-1: Prime Factorization of 72135

Prime factors of 72135 are 3, 5, 7, 229. Prime factorization of 72135 in exponential form is:

72135 = 3² × 5¹ × 7¹ × 229¹

Step-2: Prime Factorization of 72144

Prime factors of 72144 are 2, 3, 167. Prime factorization of 72144 in exponential form is:

72144 = 2⁴ × 3³ × 167¹

Step-3: Factors of 72135

List of positive integer factors of 72135 that divides 72135 without a remainder.

1, 3, 5, 7, 9, 15, 21, 35, 45, 63, 105, 229, 315, 687, 1145, 1603, 2061, 3435, 4809, 8015, 10305, 14427, 24045

Step-4: Factors of 72144

List of positive integer factors of 72144 that divides 72135 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 36, 48, 54, 72, 108, 144, 167, 216, 334, 432, 501, 668, 1002, 1336, 1503, 2004, 2672, 3006, 4008, 4509, 6012, 8016, 9018, 12024, 18036, 24048, 36072

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 72135 and 72144. The biggest common factor number is the GCF number.
So the greatest common factor 72135 and 72144 is 9.

Also check out the Least Common Multiple of 72135 and 72144