What is the Greatest Common Factor of 62385 and 62400?

Greatest common factor (GCF) of 62385 and 62400 is 15.

GCF(62385,62400) = 15

We will now calculate the prime factors of 62385 and 62400, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 62385 and 62400.

How to find the GCF of 62385 and 62400?

We will first find the prime factorization of 62385 and 62400. After we will calculate the factors of 62385 and 62400 and find the biggest common factor number .

Step-1: Prime Factorization of 62385

Prime factors of 62385 are 3, 5, 4159. Prime factorization of 62385 in exponential form is:

62385 = 3¹ × 5¹ × 4159¹

Step-2: Prime Factorization of 62400

Prime factors of 62400 are 2, 3, 5, 13. Prime factorization of 62400 in exponential form is:

62400 = 2⁶ × 3¹ × 5² × 13¹

Step-3: Factors of 62385

List of positive integer factors of 62385 that divides 62385 without a remainder.

1, 3, 5, 15, 4159, 12477, 20795

Step-4: Factors of 62400

List of positive integer factors of 62400 that divides 62385 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 13, 15, 16, 20, 24, 25, 26, 30, 32, 39, 40, 48, 50, 52, 60, 64, 65, 75, 78, 80, 96, 100, 104, 120, 130, 150, 156, 160, 192, 195, 200, 208, 240, 260, 300, 312, 320, 325, 390, 400, 416, 480, 520, 600, 624, 650, 780, 800, 832, 960, 975, 1040, 1200, 1248, 1300, 1560, 1600, 1950, 2080, 2400, 2496, 2600, 3120, 3900, 4160, 4800, 5200, 6240, 7800, 10400, 12480, 15600, 20800, 31200

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 62385 and 62400. The biggest common factor number is the GCF number.
So the greatest common factor 62385 and 62400 is 15.

Also check out the Least Common Multiple of 62385 and 62400