What is the Greatest Common Factor of 36285 and 36300?

Greatest common factor (GCF) of 36285 and 36300 is 15.

GCF(36285,36300) = 15

We will now calculate the prime factors of 36285 and 36300, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 36285 and 36300.

How to find the GCF of 36285 and 36300?

We will first find the prime factorization of 36285 and 36300. After we will calculate the factors of 36285 and 36300 and find the biggest common factor number .

Step-1: Prime Factorization of 36285

Prime factors of 36285 are 3, 5, 41, 59. Prime factorization of 36285 in exponential form is:

36285 = 3¹ × 5¹ × 41¹ × 59¹

Step-2: Prime Factorization of 36300

Prime factors of 36300 are 2, 3, 5, 11. Prime factorization of 36300 in exponential form is:

36300 = 2² × 3¹ × 5² × 11²

Step-3: Factors of 36285

List of positive integer factors of 36285 that divides 36285 without a remainder.

1, 3, 5, 15, 41, 59, 123, 177, 205, 295, 615, 885, 2419, 7257, 12095

Step-4: Factors of 36300

List of positive integer factors of 36300 that divides 36285 without a remainder.

1, 2, 3, 4, 5, 6, 10, 11, 12, 15, 20, 22, 25, 30, 33, 44, 50, 55, 60, 66, 75, 100, 110, 121, 132, 150, 165, 220, 242, 275, 300, 330, 363, 484, 550, 605, 660, 726, 825, 1100, 1210, 1452, 1650, 1815, 2420, 3025, 3300, 3630, 6050, 7260, 9075, 12100, 18150

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 36285 and 36300. The biggest common factor number is the GCF number.
So the greatest common factor 36285 and 36300 is 15.

Also check out the Least Common Multiple of 36285 and 36300