What is the Greatest Common Factor of 78300 and 78315?

Greatest common factor (GCF) of 78300 and 78315 is 15.

GCF(78300,78315) = 15

We will now calculate the prime factors of 78300 and 78315, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 78300 and 78315.

How to find the GCF of 78300 and 78315?

We will first find the prime factorization of 78300 and 78315. After we will calculate the factors of 78300 and 78315 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 78315

Prime factors of 78315 are 3, 5, 23, 227. Prime factorization of 78315 in exponential form is:

78315 = 3¹ × 5¹ × 23¹ × 227¹

Step-3: Factors of 78300

List of positive integer factors of 78300 that divides 78300 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

Step-4: Factors of 78315

List of positive integer factors of 78315 that divides 78300 without a remainder.

1, 3, 5, 15, 23, 69, 115, 227, 345, 681, 1135, 3405, 5221, 15663, 26105

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 78300 and 78315. The biggest common factor number is the GCF number.
So the greatest common factor 78300 and 78315 is 15.

Also check out the Least Common Multiple of 78300 and 78315