What is the Greatest Common Factor of 15285 and 15300?

Greatest common factor (GCF) of 15285 and 15300 is 15.

GCF(15285,15300) = 15

We will now calculate the prime factors of 15285 and 15300, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 15285 and 15300.

How to find the GCF of 15285 and 15300?

We will first find the prime factorization of 15285 and 15300. After we will calculate the factors of 15285 and 15300 and find the biggest common factor number .

Step-1: Prime Factorization of 15285

Prime factors of 15285 are 3, 5, 1019. Prime factorization of 15285 in exponential form is:

15285 = 3¹ × 5¹ × 1019¹

Step-2: Prime Factorization of 15300

Prime factors of 15300 are 2, 3, 5, 17. Prime factorization of 15300 in exponential form is:

15300 = 2² × 3² × 5² × 17¹

Step-3: Factors of 15285

List of positive integer factors of 15285 that divides 15285 without a remainder.

1, 3, 5, 15, 1019, 3057, 5095

Step-4: Factors of 15300

List of positive integer factors of 15300 that divides 15285 without a remainder.

1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 17, 18, 20, 25, 30, 34, 36, 45, 50, 51, 60, 68, 75, 85, 90, 100, 102, 150, 153, 170, 180, 204, 225, 255, 300, 306, 340, 425, 450, 510, 612, 765, 850, 900, 1020, 1275, 1530, 1700, 2550, 3060, 3825, 5100, 7650

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 15285 and 15300. The biggest common factor number is the GCF number.
So the greatest common factor 15285 and 15300 is 15.

Also check out the Least Common Multiple of 15285 and 15300