What is the Greatest Common Factor of 72075 and 72090?

Greatest common factor (GCF) of 72075 and 72090 is 15.

GCF(72075,72090) = 15

We will now calculate the prime factors of 72075 and 72090, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 72075 and 72090.

How to find the GCF of 72075 and 72090?

We will first find the prime factorization of 72075 and 72090. After we will calculate the factors of 72075 and 72090 and find the biggest common factor number .

Step-1: Prime Factorization of 72075

Prime factors of 72075 are 3, 5, 31. Prime factorization of 72075 in exponential form is:

72075 = 3¹ × 5² × 31²

Step-2: Prime Factorization of 72090

Prime factors of 72090 are 2, 3, 5, 89. Prime factorization of 72090 in exponential form is:

72090 = 2¹ × 3⁴ × 5¹ × 89¹

Step-3: Factors of 72075

List of positive integer factors of 72075 that divides 72075 without a remainder.

1, 3, 5, 15, 25, 31, 75, 93, 155, 465, 775, 961, 2325, 2883, 4805, 14415, 24025

Step-4: Factors of 72090

List of positive integer factors of 72090 that divides 72075 without a remainder.

1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 81, 89, 90, 135, 162, 178, 267, 270, 405, 445, 534, 801, 810, 890, 1335, 1602, 2403, 2670, 4005, 4806, 7209, 8010, 12015, 14418, 24030, 36045

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 72075 and 72090. The biggest common factor number is the GCF number.
So the greatest common factor 72075 and 72090 is 15.

Also check out the Least Common Multiple of 72075 and 72090