What is the Greatest Common Factor of 48384 and 48400?

Greatest common factor (GCF) of 48384 and 48400 is 16.

GCF(48384,48400) = 16

We will now calculate the prime factors of 48384 and 48400, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 48384 and 48400.

How to find the GCF of 48384 and 48400?

We will first find the prime factorization of 48384 and 48400. After we will calculate the factors of 48384 and 48400 and find the biggest common factor number .

Step-1: Prime Factorization of 48384

Prime factors of 48384 are 2, 3, 7. Prime factorization of 48384 in exponential form is:

48384 = 2⁸ × 3³ × 7¹

Step-2: Prime Factorization of 48400

Prime factors of 48400 are 2, 5, 11. Prime factorization of 48400 in exponential form is:

48400 = 2⁴ × 5² × 11²

Step-3: Factors of 48384

List of positive integer factors of 48384 that divides 48384 without a remainder.

1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 16, 18, 21, 24, 27, 28, 32, 36, 42, 48, 54, 56, 63, 64, 72, 84, 96, 108, 112, 126, 128, 144, 168, 189, 192, 216, 224, 252, 256, 288, 336, 378, 384, 432, 448, 504, 576, 672, 756, 768, 864, 896, 1008, 1152, 1344, 1512, 1728, 1792, 2016, 2304, 2688, 3024, 3456, 4032, 5376, 6048, 6912, 8064, 12096, 16128, 24192

Step-4: Factors of 48400

List of positive integer factors of 48400 that divides 48384 without a remainder.

1, 2, 4, 5, 8, 10, 11, 16, 20, 22, 25, 40, 44, 50, 55, 80, 88, 100, 110, 121, 176, 200, 220, 242, 275, 400, 440, 484, 550, 605, 880, 968, 1100, 1210, 1936, 2200, 2420, 3025, 4400, 4840, 6050, 9680, 12100, 24200

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 48384 and 48400. The biggest common factor number is the GCF number.
So the greatest common factor 48384 and 48400 is 16.

Also check out the Least Common Multiple of 48384 and 48400