What is the Greatest Common Factor of 15300 and 15314?

Greatest common factor (GCF) of 15300 and 15314 is 2.

GCF(15300,15314) = 2

We will now calculate the prime factors of 15300 and 15314, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 15300 and 15314.

How to find the GCF of 15300 and 15314?

We will first find the prime factorization of 15300 and 15314. After we will calculate the factors of 15300 and 15314 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 15314

Prime factors of 15314 are 2, 13, 19, 31. Prime factorization of 15314 in exponential form is:

15314 = 2¹ × 13¹ × 19¹ × 31¹

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 15314

List of positive integer factors of 15314 that divides 15300 without a remainder.

1, 2, 13, 19, 26, 31, 38, 62, 247, 403, 494, 589, 806, 1178, 7657

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 15300 and 15314. The biggest common factor number is the GCF number.
So the greatest common factor 15300 and 15314 is 2.

Also check out the Least Common Multiple of 15300 and 15314