What is the Greatest Common Factor of 58305 and 58320?

Greatest common factor (GCF) of 58305 and 58320 is 15.

GCF(58305,58320) = 15

We will now calculate the prime factors of 58305 and 58320, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 58305 and 58320.

How to find the GCF of 58305 and 58320?

We will first find the prime factorization of 58305 and 58320. After we will calculate the factors of 58305 and 58320 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 58320

Prime factors of 58320 are 2, 3, 5. Prime factorization of 58320 in exponential form is:

58320 = 2⁴ × 3⁶ × 5¹

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 58320

List of positive integer factors of 58320 that divides 58305 without a remainder.

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 27, 30, 36, 40, 45, 48, 54, 60, 72, 80, 81, 90, 108, 120, 135, 144, 162, 180, 216, 240, 243, 270, 324, 360, 405, 432, 486, 540, 648, 720, 729, 810, 972, 1080, 1215, 1296, 1458, 1620, 1944, 2160, 2430, 2916, 3240, 3645, 3888, 4860, 5832, 6480, 7290, 9720, 11664, 14580, 19440, 29160

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 58305 and 58320. The biggest common factor number is the GCF number.
So the greatest common factor 58305 and 58320 is 15.

Also check out the Least Common Multiple of 58305 and 58320