What is the Greatest Common Factor of 92385 and 92400?

Greatest common factor (GCF) of 92385 and 92400 is 15.

GCF(92385,92400) = 15

We will now calculate the prime factors of 92385 and 92400, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 92385 and 92400.

How to find the GCF of 92385 and 92400?

We will first find the prime factorization of 92385 and 92400. After we will calculate the factors of 92385 and 92400 and find the biggest common factor number .

Step-1: Prime Factorization of 92385

Prime factors of 92385 are 3, 5, 2053. Prime factorization of 92385 in exponential form is:

92385 = 3² × 5¹ × 2053¹

Step-2: Prime Factorization of 92400

Prime factors of 92400 are 2, 3, 5, 7, 11. Prime factorization of 92400 in exponential form is:

92400 = 2⁴ × 3¹ × 5² × 7¹ × 11¹

Step-3: Factors of 92385

List of positive integer factors of 92385 that divides 92385 without a remainder.

1, 3, 5, 9, 15, 45, 2053, 6159, 10265, 18477, 30795

Step-4: Factors of 92400

List of positive integer factors of 92400 that divides 92385 without a remainder.

1, 2, 3, 4, 5, 6, 7, 8, 10, 11, 12, 14, 15, 16, 20, 21, 22, 24, 25, 28, 30, 33, 35, 40, 42, 44, 48, 50, 55, 56, 60, 66, 70, 75, 77, 80, 84, 88, 100, 105, 110, 112, 120, 132, 140, 150, 154, 165, 168, 175, 176, 200, 210, 220, 231, 240, 264, 275, 280, 300, 308, 330, 336, 350, 385, 400, 420, 440, 462, 525, 528, 550, 560, 600, 616, 660, 700, 770, 825, 840, 880, 924, 1050, 1100, 1155, 1200, 1232, 1320, 1400, 1540, 1650, 1680, 1848, 1925, 2100, 2200, 2310, 2640, 2800, 3080, 3300, 3696, 3850, 4200, 4400, 4620, 5775, 6160, 6600, 7700, 8400, 9240, 11550, 13200, 15400, 18480, 23100, 30800, 46200

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 92385 and 92400. The biggest common factor number is the GCF number.
So the greatest common factor 92385 and 92400 is 15.

Also check out the Least Common Multiple of 92385 and 92400