What is the Greatest Common Factor of 76400 and 76415?

Greatest common factor (GCF) of 76400 and 76415 is 5.

GCF(76400,76415) = 5

We will now calculate the prime factors of 76400 and 76415, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 76400 and 76415.

How to find the GCF of 76400 and 76415?

We will first find the prime factorization of 76400 and 76415. After we will calculate the factors of 76400 and 76415 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 76415

Prime factors of 76415 are 5, 17, 29, 31. Prime factorization of 76415 in exponential form is:

76415 = 5¹ × 17¹ × 29¹ × 31¹

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 76415

List of positive integer factors of 76415 that divides 76400 without a remainder.

1, 5, 17, 29, 31, 85, 145, 155, 493, 527, 899, 2465, 2635, 4495, 15283

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 76400 and 76415. The biggest common factor number is the GCF number.
So the greatest common factor 76400 and 76415 is 5.

Also check out the Least Common Multiple of 76400 and 76415