What is the Greatest Common Factor of 78385 and 78400?

Greatest common factor (GCF) of 78385 and 78400 is 5.

GCF(78385,78400) = 5

We will now calculate the prime factors of 78385 and 78400, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 78385 and 78400.

How to find the GCF of 78385 and 78400?

We will first find the prime factorization of 78385 and 78400. After we will calculate the factors of 78385 and 78400 and find the biggest common factor number .

Step-1: Prime Factorization of 78385

Prime factors of 78385 are 5, 61, 257. Prime factorization of 78385 in exponential form is:

78385 = 5¹ × 61¹ × 257¹

Step-2: 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-3: Factors of 78385

List of positive integer factors of 78385 that divides 78385 without a remainder.

1, 5, 61, 257, 305, 1285, 15677

Step-4: Factors of 78400

List of positive integer factors of 78400 that divides 78385 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 78385 and 78400. The biggest common factor number is the GCF number.
So the greatest common factor 78385 and 78400 is 5.

Also check out the Least Common Multiple of 78385 and 78400