What is the Greatest Common Factor of 78400 and 78404?

Greatest common factor (GCF) of 78400 and 78404 is 4.

GCF(78400,78404) = 4

We will now calculate the prime factors of 78400 and 78404, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 78400 and 78404.

How to find the GCF of 78400 and 78404?

We will first find the prime factorization of 78400 and 78404. After we will calculate the factors of 78400 and 78404 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 78404

Prime factors of 78404 are 2, 17, 1153. Prime factorization of 78404 in exponential form is:

78404 = 2² × 17¹ × 1153¹

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 78404

List of positive integer factors of 78404 that divides 78400 without a remainder.

1, 2, 4, 17, 34, 68, 1153, 2306, 4612, 19601, 39202

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 78400 and 78404. The biggest common factor number is the GCF number.
So the greatest common factor 78400 and 78404 is 4.

Also check out the Least Common Multiple of 78400 and 78404