What is the Greatest Common Factor of 15300 and 15309?

Greatest common factor (GCF) of 15300 and 15309 is 9.

GCF(15300,15309) = 9

We will now calculate the prime factors of 15300 and 15309, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 15300 and 15309.

How to find the GCF of 15300 and 15309?

We will first find the prime factorization of 15300 and 15309. After we will calculate the factors of 15300 and 15309 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 15309

Prime factors of 15309 are 3, 7. Prime factorization of 15309 in exponential form is:

15309 = 3⁷ × 7¹

Step-3: Factors of 15300

List of positive integer factors of 15300 that divides 15300 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

Step-4: Factors of 15309

List of positive integer factors of 15309 that divides 15300 without a remainder.

1, 3, 7, 9, 21, 27, 63, 81, 189, 243, 567, 729, 1701, 2187, 5103

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 15300 and 15309. The biggest common factor number is the GCF number.
So the greatest common factor 15300 and 15309 is 9.

Also check out the Least Common Multiple of 15300 and 15309