What is the Greatest Common Factor of 78400 and 78415?

Greatest common factor (GCF) of 78400 and 78415 is 5.

GCF(78400,78415) = 5

We will now calculate the prime factors of 78400 and 78415, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 78400 and 78415.

How to find the GCF of 78400 and 78415?

We will first find the prime factorization of 78400 and 78415. After we will calculate the factors of 78400 and 78415 and find the biggest common factor number .

Step-1: Prime Factorization of 78400

Prime factors of 78400 are 2, 5, 7. Prime factorization of 78400 in exponential form is:

78400 = 2⁶ × 5² × 7²

Step-2: Prime Factorization of 78415

Prime factors of 78415 are 5, 15683. Prime factorization of 78415 in exponential form is:

78415 = 5¹ × 15683¹

Step-3: Factors of 78400

List of positive integer factors of 78400 that divides 78400 without a remainder.

1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 25, 28, 32, 35, 40, 49, 50, 56, 64, 70, 80, 98, 100, 112, 140, 160, 175, 196, 200, 224, 245, 280, 320, 350, 392, 400, 448, 490, 560, 700, 784, 800, 980, 1120, 1225, 1400, 1568, 1600, 1960, 2240, 2450, 2800, 3136, 3920, 4900, 5600, 7840, 9800, 11200, 15680, 19600, 39200

Step-4: Factors of 78415

List of positive integer factors of 78415 that divides 78400 without a remainder.

1, 5, 15683

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 78400 and 78415. The biggest common factor number is the GCF number.
So the greatest common factor 78400 and 78415 is 5.

Also check out the Least Common Multiple of 78400 and 78415