What is the Greatest Common Factor of 27285 and 27300?

Greatest common factor (GCF) of 27285 and 27300 is 15.

GCF(27285,27300) = 15

We will now calculate the prime factors of 27285 and 27300, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 27285 and 27300.

How to find the GCF of 27285 and 27300?

We will first find the prime factorization of 27285 and 27300. After we will calculate the factors of 27285 and 27300 and find the biggest common factor number .

Step-1: Prime Factorization of 27285

Prime factors of 27285 are 3, 5, 17, 107. Prime factorization of 27285 in exponential form is:

27285 = 3¹ × 5¹ × 17¹ × 107¹

Step-2: 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-3: Factors of 27285

List of positive integer factors of 27285 that divides 27285 without a remainder.

1, 3, 5, 15, 17, 51, 85, 107, 255, 321, 535, 1605, 1819, 5457, 9095

Step-4: Factors of 27300

List of positive integer factors of 27300 that divides 27285 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 27285 and 27300. The biggest common factor number is the GCF number.
So the greatest common factor 27285 and 27300 is 15.

Also check out the Least Common Multiple of 27285 and 27300