What is the Greatest Common Factor of 48384 and 48398?

Greatest common factor (GCF) of 48384 and 48398 is 14.

GCF(48384,48398) = 14

We will now calculate the prime factors of 48384 and 48398, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 48384 and 48398.

How to find the GCF of 48384 and 48398?

We will first find the prime factorization of 48384 and 48398. After we will calculate the factors of 48384 and 48398 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 48398

Prime factors of 48398 are 2, 7, 3457. Prime factorization of 48398 in exponential form is:

48398 = 2¹ × 7¹ × 3457¹

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 48398

List of positive integer factors of 48398 that divides 48384 without a remainder.

1, 2, 7, 14, 3457, 6914, 24199

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 48384 and 48398. The biggest common factor number is the GCF number.
So the greatest common factor 48384 and 48398 is 14.

Also check out the Least Common Multiple of 48384 and 48398