What is the Greatest Common Factor of 30400 and 30407?

Greatest common factor (GCF) of 30400 and 30407 is 1.

GCF(30400,30407) = 1

We will now calculate the prime factors of 30400 and 30407, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30400 and 30407.

How to find the GCF of 30400 and 30407?

We will first find the prime factorization of 30400 and 30407. After we will calculate the factors of 30400 and 30407 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 30407

Prime factors of 30407 are 13, 2339. Prime factorization of 30407 in exponential form is:

30407 = 13¹ × 2339¹

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 30407

List of positive integer factors of 30407 that divides 30400 without a remainder.

1, 13, 2339

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30400 and 30407. The biggest common factor number is the GCF number.
So the greatest common factor 30400 and 30407 is 1.

Also check out the Least Common Multiple of 30400 and 30407