What is the Greatest Common Factor of 90285 and 90300?

Greatest common factor (GCF) of 90285 and 90300 is 15.

GCF(90285,90300) = 15

We will now calculate the prime factors of 90285 and 90300, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 90285 and 90300.

How to find the GCF of 90285 and 90300?

We will first find the prime factorization of 90285 and 90300. After we will calculate the factors of 90285 and 90300 and find the biggest common factor number .

Step-1: Prime Factorization of 90285

Prime factors of 90285 are 3, 5, 13, 463. Prime factorization of 90285 in exponential form is:

90285 = 3¹ × 5¹ × 13¹ × 463¹

Step-2: Prime Factorization of 90300

Prime factors of 90300 are 2, 3, 5, 7, 43. Prime factorization of 90300 in exponential form is:

90300 = 2² × 3¹ × 5² × 7¹ × 43¹

Step-3: Factors of 90285

List of positive integer factors of 90285 that divides 90285 without a remainder.

1, 3, 5, 13, 15, 39, 65, 195, 463, 1389, 2315, 6019, 6945, 18057, 30095

Step-4: Factors of 90300

List of positive integer factors of 90300 that divides 90285 without a remainder.

1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 25, 28, 30, 35, 42, 43, 50, 60, 70, 75, 84, 86, 100, 105, 129, 140, 150, 172, 175, 210, 215, 258, 300, 301, 350, 420, 430, 516, 525, 602, 645, 700, 860, 903, 1050, 1075, 1204, 1290, 1505, 1806, 2100, 2150, 2580, 3010, 3225, 3612, 4300, 4515, 6020, 6450, 7525, 9030, 12900, 15050, 18060, 22575, 30100, 45150

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 90285 and 90300. The biggest common factor number is the GCF number.
So the greatest common factor 90285 and 90300 is 15.

Also check out the Least Common Multiple of 90285 and 90300