What is the Greatest Common Factor of 27300 and 27309?

Greatest common factor (GCF) of 27300 and 27309 is 3.

GCF(27300,27309) = 3

We will now calculate the prime factors of 27300 and 27309, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 27300 and 27309.

How to find the GCF of 27300 and 27309?

We will first find the prime factorization of 27300 and 27309. After we will calculate the factors of 27300 and 27309 and find the biggest common factor number .

Step-1: Prime Factorization of 27300

Prime factors of 27300 are 2, 3, 5, 7, 13. Prime factorization of 27300 in exponential form is:

27300 = 2² × 3¹ × 5² × 7¹ × 13¹

Step-2: Prime Factorization of 27309

Prime factors of 27309 are 3, 9103. Prime factorization of 27309 in exponential form is:

27309 = 3¹ × 9103¹

Step-3: Factors of 27300

List of positive integer factors of 27300 that divides 27300 without a remainder.

1, 2, 3, 4, 5, 6, 7, 10, 12, 13, 14, 15, 20, 21, 25, 26, 28, 30, 35, 39, 42, 50, 52, 60, 65, 70, 75, 78, 84, 91, 100, 105, 130, 140, 150, 156, 175, 182, 195, 210, 260, 273, 300, 325, 350, 364, 390, 420, 455, 525, 546, 650, 700, 780, 910, 975, 1050, 1092, 1300, 1365, 1820, 1950, 2100, 2275, 2730, 3900, 4550, 5460, 6825, 9100, 13650

Step-4: Factors of 27309

List of positive integer factors of 27309 that divides 27300 without a remainder.

1, 3, 9103

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 27300 and 27309. The biggest common factor number is the GCF number.
So the greatest common factor 27300 and 27309 is 3.

Also check out the Least Common Multiple of 27300 and 27309