What is the Greatest Common Factor of 86385 and 86400?

Greatest common factor (GCF) of 86385 and 86400 is 15.

GCF(86385,86400) = 15

We will now calculate the prime factors of 86385 and 86400, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 86385 and 86400.

How to find the GCF of 86385 and 86400?

We will first find the prime factorization of 86385 and 86400. After we will calculate the factors of 86385 and 86400 and find the biggest common factor number .

Step-1: Prime Factorization of 86385

Prime factors of 86385 are 3, 5, 13, 443. Prime factorization of 86385 in exponential form is:

86385 = 3¹ × 5¹ × 13¹ × 443¹

Step-2: Prime Factorization of 86400

Prime factors of 86400 are 2, 3, 5. Prime factorization of 86400 in exponential form is:

86400 = 2⁷ × 3³ × 5²

Step-3: Factors of 86385

List of positive integer factors of 86385 that divides 86385 without a remainder.

1, 3, 5, 13, 15, 39, 65, 195, 443, 1329, 2215, 5759, 6645, 17277, 28795

Step-4: Factors of 86400

List of positive integer factors of 86400 that divides 86385 without a remainder.

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 25, 27, 30, 32, 36, 40, 45, 48, 50, 54, 60, 64, 72, 75, 80, 90, 96, 100, 108, 120, 128, 135, 144, 150, 160, 180, 192, 200, 216, 225, 240, 270, 288, 300, 320, 360, 384, 400, 432, 450, 480, 540, 576, 600, 640, 675, 720, 800, 864, 900, 960, 1080, 1152, 1200, 1350, 1440, 1600, 1728, 1800, 1920, 2160, 2400, 2700, 2880, 3200, 3456, 3600, 4320, 4800, 5400, 5760, 7200, 8640, 9600, 10800, 14400, 17280, 21600, 28800, 43200

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 86385 and 86400. The biggest common factor number is the GCF number.
So the greatest common factor 86385 and 86400 is 15.

Also check out the Least Common Multiple of 86385 and 86400