What is the Greatest Common Factor of 78285 and 78300?

Greatest common factor (GCF) of 78285 and 78300 is 15.

GCF(78285,78300) = 15

We will now calculate the prime factors of 78285 and 78300, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 78285 and 78300.

How to find the GCF of 78285 and 78300?

We will first find the prime factorization of 78285 and 78300. After we will calculate the factors of 78285 and 78300 and find the biggest common factor number .

Step-1: Prime Factorization of 78285

Prime factors of 78285 are 3, 5, 17, 307. Prime factorization of 78285 in exponential form is:

78285 = 3¹ × 5¹ × 17¹ × 307¹

Step-2: Prime Factorization of 78300

Prime factors of 78300 are 2, 3, 5, 29. Prime factorization of 78300 in exponential form is:

78300 = 2² × 3³ × 5² × 29¹

Step-3: Factors of 78285

List of positive integer factors of 78285 that divides 78285 without a remainder.

1, 3, 5, 15, 17, 51, 85, 255, 307, 921, 1535, 4605, 5219, 15657, 26095

Step-4: Factors of 78300

List of positive integer factors of 78300 that divides 78285 without a remainder.

1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 25, 27, 29, 30, 36, 45, 50, 54, 58, 60, 75, 87, 90, 100, 108, 116, 135, 145, 150, 174, 180, 225, 261, 270, 290, 300, 348, 435, 450, 522, 540, 580, 675, 725, 783, 870, 900, 1044, 1305, 1350, 1450, 1566, 1740, 2175, 2610, 2700, 2900, 3132, 3915, 4350, 5220, 6525, 7830, 8700, 13050, 15660, 19575, 26100, 39150

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 78285 and 78300. The biggest common factor number is the GCF number.
So the greatest common factor 78285 and 78300 is 15.

Also check out the Least Common Multiple of 78285 and 78300