What is the Greatest Common Factor of 50385 and 50400?

Greatest common factor (GCF) of 50385 and 50400 is 15.

GCF(50385,50400) = 15

We will now calculate the prime factors of 50385 and 50400, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 50385 and 50400.

How to find the GCF of 50385 and 50400?

We will first find the prime factorization of 50385 and 50400. After we will calculate the factors of 50385 and 50400 and find the biggest common factor number .

Step-1: Prime Factorization of 50385

Prime factors of 50385 are 3, 5, 3359. Prime factorization of 50385 in exponential form is:

50385 = 3¹ × 5¹ × 3359¹

Step-2: Prime Factorization of 50400

Prime factors of 50400 are 2, 3, 5, 7. Prime factorization of 50400 in exponential form is:

50400 = 2⁵ × 3² × 5² × 7¹

Step-3: Factors of 50385

List of positive integer factors of 50385 that divides 50385 without a remainder.

1, 3, 5, 15, 3359, 10077, 16795

Step-4: Factors of 50400

List of positive integer factors of 50400 that divides 50385 without a remainder.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 24, 25, 28, 30, 32, 35, 36, 40, 42, 45, 48, 50, 56, 60, 63, 70, 72, 75, 80, 84, 90, 96, 100, 105, 112, 120, 126, 140, 144, 150, 160, 168, 175, 180, 200, 210, 224, 225, 240, 252, 280, 288, 300, 315, 336, 350, 360, 400, 420, 450, 480, 504, 525, 560, 600, 630, 672, 700, 720, 800, 840, 900, 1008, 1050, 1120, 1200, 1260, 1400, 1440, 1575, 1680, 1800, 2016, 2100, 2400, 2520, 2800, 3150, 3360, 3600, 4200, 5040, 5600, 6300, 7200, 8400, 10080, 12600, 16800, 25200

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 50385 and 50400. The biggest common factor number is the GCF number.
So the greatest common factor 50385 and 50400 is 15.

Also check out the Least Common Multiple of 50385 and 50400