What is the Greatest Common Factor of 30400 and 30406?

Greatest common factor (GCF) of 30400 and 30406 is 2.

GCF(30400,30406) = 2

We will now calculate the prime factors of 30400 and 30406, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30400 and 30406.

How to find the GCF of 30400 and 30406?

We will first find the prime factorization of 30400 and 30406. After we will calculate the factors of 30400 and 30406 and find the biggest common factor number .

Step-1: Prime Factorization of 30400

Prime factors of 30400 are 2, 5, 19. Prime factorization of 30400 in exponential form is:

30400 = 2⁶ × 5² × 19¹

Step-2: Prime Factorization of 30406

Prime factors of 30406 are 2, 23, 661. Prime factorization of 30406 in exponential form is:

30406 = 2¹ × 23¹ × 661¹

Step-3: Factors of 30400

List of positive integer factors of 30400 that divides 30400 without a remainder.

1, 2, 4, 5, 8, 10, 16, 19, 20, 25, 32, 38, 40, 50, 64, 76, 80, 95, 100, 152, 160, 190, 200, 304, 320, 380, 400, 475, 608, 760, 800, 950, 1216, 1520, 1600, 1900, 3040, 3800, 6080, 7600, 15200

Step-4: Factors of 30406

List of positive integer factors of 30406 that divides 30400 without a remainder.

1, 2, 23, 46, 661, 1322, 15203

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30400 and 30406. The biggest common factor number is the GCF number.
So the greatest common factor 30400 and 30406 is 2.

Also check out the Least Common Multiple of 30400 and 30406