What is the Greatest Common Factor of 58200 and 58214?

Greatest common factor (GCF) of 58200 and 58214 is 2.

GCF(58200,58214) = 2

We will now calculate the prime factors of 58200 and 58214, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 58200 and 58214.

How to find the GCF of 58200 and 58214?

We will first find the prime factorization of 58200 and 58214. After we will calculate the factors of 58200 and 58214 and find the biggest common factor number .

Step-1: Prime Factorization of 58200

Prime factors of 58200 are 2, 3, 5, 97. Prime factorization of 58200 in exponential form is:

58200 = 2³ × 3¹ × 5² × 97¹

Step-2: Prime Factorization of 58214

Prime factors of 58214 are 2, 13, 2239. Prime factorization of 58214 in exponential form is:

58214 = 2¹ × 13¹ × 2239¹

Step-3: Factors of 58200

List of positive integer factors of 58200 that divides 58200 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 25, 30, 40, 50, 60, 75, 97, 100, 120, 150, 194, 200, 291, 300, 388, 485, 582, 600, 776, 970, 1164, 1455, 1940, 2328, 2425, 2910, 3880, 4850, 5820, 7275, 9700, 11640, 14550, 19400, 29100

Step-4: Factors of 58214

List of positive integer factors of 58214 that divides 58200 without a remainder.

1, 2, 13, 26, 2239, 4478, 29107

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 58200 and 58214. The biggest common factor number is the GCF number.
So the greatest common factor 58200 and 58214 is 2.

Also check out the Least Common Multiple of 58200 and 58214