What is the Greatest Common Factor of 76384 and 76400?

Greatest common factor (GCF) of 76384 and 76400 is 16.

GCF(76384,76400) = 16

We will now calculate the prime factors of 76384 and 76400, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 76384 and 76400.

How to find the GCF of 76384 and 76400?

We will first find the prime factorization of 76384 and 76400. After we will calculate the factors of 76384 and 76400 and find the biggest common factor number .

Step-1: Prime Factorization of 76384

Prime factors of 76384 are 2, 7, 11, 31. Prime factorization of 76384 in exponential form is:

76384 = 2⁵ × 7¹ × 11¹ × 31¹

Step-2: Prime Factorization of 76400

Prime factors of 76400 are 2, 5, 191. Prime factorization of 76400 in exponential form is:

76400 = 2⁴ × 5² × 191¹

Step-3: Factors of 76384

List of positive integer factors of 76384 that divides 76384 without a remainder.

1, 2, 4, 7, 8, 11, 14, 16, 22, 28, 31, 32, 44, 56, 62, 77, 88, 112, 124, 154, 176, 217, 224, 248, 308, 341, 352, 434, 496, 616, 682, 868, 992, 1232, 1364, 1736, 2387, 2464, 2728, 3472, 4774, 5456, 6944, 9548, 10912, 19096, 38192

Step-4: Factors of 76400

List of positive integer factors of 76400 that divides 76384 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 191, 200, 382, 400, 764, 955, 1528, 1910, 3056, 3820, 4775, 7640, 9550, 15280, 19100, 38200

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 76384 and 76400. The biggest common factor number is the GCF number.
So the greatest common factor 76384 and 76400 is 16.

Also check out the Least Common Multiple of 76384 and 76400