What is the Greatest Common Factor of 30400 and 30414?

Greatest common factor (GCF) of 30400 and 30414 is 2.

GCF(30400,30414) = 2

We will now calculate the prime factors of 30400 and 30414, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30400 and 30414.

How to find the GCF of 30400 and 30414?

We will first find the prime factorization of 30400 and 30414. After we will calculate the factors of 30400 and 30414 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 30414

Prime factors of 30414 are 2, 3, 37, 137. Prime factorization of 30414 in exponential form is:

30414 = 2¹ × 3¹ × 37¹ × 137¹

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 30414

List of positive integer factors of 30414 that divides 30400 without a remainder.

1, 2, 3, 6, 37, 74, 111, 137, 222, 274, 411, 822, 5069, 10138, 15207

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30400 and 30414. The biggest common factor number is the GCF number.
So the greatest common factor 30400 and 30414 is 2.

Also check out the Least Common Multiple of 30400 and 30414