What is the Greatest Common Factor of 15300 and 15306?

Greatest common factor (GCF) of 15300 and 15306 is 6.

GCF(15300,15306) = 6

We will now calculate the prime factors of 15300 and 15306, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 15300 and 15306.

How to find the GCF of 15300 and 15306?

We will first find the prime factorization of 15300 and 15306. After we will calculate the factors of 15300 and 15306 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 15306

Prime factors of 15306 are 2, 3, 2551. Prime factorization of 15306 in exponential form is:

15306 = 2¹ × 3¹ × 2551¹

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 15306

List of positive integer factors of 15306 that divides 15300 without a remainder.

1, 2, 3, 6, 2551, 5102, 7653

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 15300 and 15306. The biggest common factor number is the GCF number.
So the greatest common factor 15300 and 15306 is 6.

Also check out the Least Common Multiple of 15300 and 15306