What is the Greatest Common Factor of 30385 and 30400?

Greatest common factor (GCF) of 30385 and 30400 is 5.

GCF(30385,30400) = 5

We will now calculate the prime factors of 30385 and 30400, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30385 and 30400.

How to find the GCF of 30385 and 30400?

We will first find the prime factorization of 30385 and 30400. After we will calculate the factors of 30385 and 30400 and find the biggest common factor number .

Step-1: Prime Factorization of 30385

Prime factors of 30385 are 5, 59, 103. Prime factorization of 30385 in exponential form is:

30385 = 5¹ × 59¹ × 103¹

Step-2: 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-3: Factors of 30385

List of positive integer factors of 30385 that divides 30385 without a remainder.

1, 5, 59, 103, 295, 515, 6077

Step-4: Factors of 30400

List of positive integer factors of 30400 that divides 30385 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30385 and 30400. The biggest common factor number is the GCF number.
So the greatest common factor 30385 and 30400 is 5.

Also check out the Least Common Multiple of 30385 and 30400