What is the Greatest Common Factor of 50400 and 50414?

Greatest common factor (GCF) of 50400 and 50414 is 14.

GCF(50400,50414) = 14

We will now calculate the prime factors of 50400 and 50414, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 50400 and 50414.

How to find the GCF of 50400 and 50414?

We will first find the prime factorization of 50400 and 50414. After we will calculate the factors of 50400 and 50414 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 50414

Prime factors of 50414 are 2, 7, 13, 277. Prime factorization of 50414 in exponential form is:

50414 = 2¹ × 7¹ × 13¹ × 277¹

Step-3: Factors of 50400

List of positive integer factors of 50400 that divides 50400 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

Step-4: Factors of 50414

List of positive integer factors of 50414 that divides 50400 without a remainder.

1, 2, 7, 13, 14, 26, 91, 182, 277, 554, 1939, 3601, 3878, 7202, 25207

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 50400 and 50414. The biggest common factor number is the GCF number.
So the greatest common factor 50400 and 50414 is 14.

Also check out the Least Common Multiple of 50400 and 50414