What is the Greatest Common Factor of 58400 and 58414?

Greatest common factor (GCF) of 58400 and 58414 is 2.

GCF(58400,58414) = 2

We will now calculate the prime factors of 58400 and 58414, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 58400 and 58414.

How to find the GCF of 58400 and 58414?

We will first find the prime factorization of 58400 and 58414. After we will calculate the factors of 58400 and 58414 and find the biggest common factor number .

Step-1: Prime Factorization of 58400

Prime factors of 58400 are 2, 5, 73. Prime factorization of 58400 in exponential form is:

58400 = 2⁵ × 5² × 73¹

Step-2: Prime Factorization of 58414

Prime factors of 58414 are 2, 29207. Prime factorization of 58414 in exponential form is:

58414 = 2¹ × 29207¹

Step-3: Factors of 58400

List of positive integer factors of 58400 that divides 58400 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 73, 80, 100, 146, 160, 200, 292, 365, 400, 584, 730, 800, 1168, 1460, 1825, 2336, 2920, 3650, 5840, 7300, 11680, 14600, 29200

Step-4: Factors of 58414

List of positive integer factors of 58414 that divides 58400 without a remainder.

1, 2, 29207

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 58400 and 58414. The biggest common factor number is the GCF number.
So the greatest common factor 58400 and 58414 is 2.

Also check out the Least Common Multiple of 58400 and 58414