What is the Greatest Common Factor of 58305 and 58312?

Greatest common factor (GCF) of 58305 and 58312 is 1.

GCF(58305,58312) = 1

We will now calculate the prime factors of 58305 and 58312, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 58305 and 58312.

How to find the GCF of 58305 and 58312?

We will first find the prime factorization of 58305 and 58312. After we will calculate the factors of 58305 and 58312 and find the biggest common factor number .

Step-1: Prime Factorization of 58305

Prime factors of 58305 are 3, 5, 13, 23. Prime factorization of 58305 in exponential form is:

58305 = 3¹ × 5¹ × 13² × 23¹

Step-2: Prime Factorization of 58312

Prime factors of 58312 are 2, 37, 197. Prime factorization of 58312 in exponential form is:

58312 = 2³ × 37¹ × 197¹

Step-3: Factors of 58305

List of positive integer factors of 58305 that divides 58305 without a remainder.

1, 3, 5, 13, 15, 23, 39, 65, 69, 115, 169, 195, 299, 345, 507, 845, 897, 1495, 2535, 3887, 4485, 11661, 19435

Step-4: Factors of 58312

List of positive integer factors of 58312 that divides 58305 without a remainder.

1, 2, 4, 8, 37, 74, 148, 197, 296, 394, 788, 1576, 7289, 14578, 29156

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 58305 and 58312. The biggest common factor number is the GCF number.
So the greatest common factor 58305 and 58312 is 1.

Also check out the Least Common Multiple of 58305 and 58312