What is the Greatest Common Factor of 58314 and 58320?

Greatest common factor (GCF) of 58314 and 58320 is 6.

GCF(58314,58320) = 6

We will now calculate the prime factors of 58314 and 58320, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 58314 and 58320.

How to find the GCF of 58314 and 58320?

We will first find the prime factorization of 58314 and 58320. After we will calculate the factors of 58314 and 58320 and find the biggest common factor number .

Step-1: Prime Factorization of 58314

Prime factors of 58314 are 2, 3, 9719. Prime factorization of 58314 in exponential form is:

58314 = 2¹ × 3¹ × 9719¹

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 58314

List of positive integer factors of 58314 that divides 58314 without a remainder.

1, 2, 3, 6, 9719, 19438, 29157

Step-4: Factors of 58320

List of positive integer factors of 58320 that divides 58314 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 58314 and 58320. The biggest common factor number is the GCF number.
So the greatest common factor 58314 and 58320 is 6.

Also check out the Least Common Multiple of 58314 and 58320