What is the Greatest Common Factor of 76400 and 76416?

Greatest common factor (GCF) of 76400 and 76416 is 16.

GCF(76400,76416) = 16

We will now calculate the prime factors of 76400 and 76416, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 76400 and 76416.

How to find the GCF of 76400 and 76416?

We will first find the prime factorization of 76400 and 76416. After we will calculate the factors of 76400 and 76416 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 76416

Prime factors of 76416 are 2, 3, 199. Prime factorization of 76416 in exponential form is:

76416 = 2⁷ × 3¹ × 199¹

Step-3: Factors of 76400

List of positive integer factors of 76400 that divides 76400 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

Step-4: Factors of 76416

List of positive integer factors of 76416 that divides 76400 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 199, 384, 398, 597, 796, 1194, 1592, 2388, 3184, 4776, 6368, 9552, 12736, 19104, 25472, 38208

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 76400 and 76416. The biggest common factor number is the GCF number.
So the greatest common factor 76400 and 76416 is 16.

Also check out the Least Common Multiple of 76400 and 76416