What is the Greatest Common Factor of 69285 and 69300?

Greatest common factor (GCF) of 69285 and 69300 is 15.

GCF(69285,69300) = 15

We will now calculate the prime factors of 69285 and 69300, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 69285 and 69300.

How to find the GCF of 69285 and 69300?

We will first find the prime factorization of 69285 and 69300. After we will calculate the factors of 69285 and 69300 and find the biggest common factor number .

Step-1: Prime Factorization of 69285

Prime factors of 69285 are 3, 5, 31, 149. Prime factorization of 69285 in exponential form is:

69285 = 3¹ × 5¹ × 31¹ × 149¹

Step-2: Prime Factorization of 69300

Prime factors of 69300 are 2, 3, 5, 7, 11. Prime factorization of 69300 in exponential form is:

69300 = 2² × 3² × 5² × 7¹ × 11¹

Step-3: Factors of 69285

List of positive integer factors of 69285 that divides 69285 without a remainder.

1, 3, 5, 15, 31, 93, 149, 155, 447, 465, 745, 2235, 4619, 13857, 23095

Step-4: Factors of 69300

List of positive integer factors of 69300 that divides 69285 without a remainder.

1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 14, 15, 18, 20, 21, 22, 25, 28, 30, 33, 35, 36, 42, 44, 45, 50, 55, 60, 63, 66, 70, 75, 77, 84, 90, 99, 100, 105, 110, 126, 132, 140, 150, 154, 165, 175, 180, 198, 210, 220, 225, 231, 252, 275, 300, 308, 315, 330, 350, 385, 396, 420, 450, 462, 495, 525, 550, 630, 660, 693, 700, 770, 825, 900, 924, 990, 1050, 1100, 1155, 1260, 1386, 1540, 1575, 1650, 1925, 1980, 2100, 2310, 2475, 2772, 3150, 3300, 3465, 3850, 4620, 4950, 5775, 6300, 6930, 7700, 9900, 11550, 13860, 17325, 23100, 34650

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 69285 and 69300. The biggest common factor number is the GCF number.
So the greatest common factor 69285 and 69300 is 15.

Also check out the Least Common Multiple of 69285 and 69300