What is the Greatest Common Factor of 30400 and 30416?

Greatest common factor (GCF) of 30400 and 30416 is 16.

GCF(30400,30416) = 16

We will now calculate the prime factors of 30400 and 30416, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30400 and 30416.

How to find the GCF of 30400 and 30416?

We will first find the prime factorization of 30400 and 30416. After we will calculate the factors of 30400 and 30416 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 30416

Prime factors of 30416 are 2, 1901. Prime factorization of 30416 in exponential form is:

30416 = 2⁴ × 1901¹

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 30416

List of positive integer factors of 30416 that divides 30400 without a remainder.

1, 2, 4, 8, 16, 1901, 3802, 7604, 15208

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30400 and 30416. The biggest common factor number is the GCF number.
So the greatest common factor 30400 and 30416 is 16.

Also check out the Least Common Multiple of 30400 and 30416