What is the Greatest Common Factor of 58320 and 58338?

Greatest common factor (GCF) of 58320 and 58338 is 18.

GCF(58320,58338) = 18

We will now calculate the prime factors of 58320 and 58338, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 58320 and 58338.

How to find the GCF of 58320 and 58338?

We will first find the prime factorization of 58320 and 58338. After we will calculate the factors of 58320 and 58338 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 58338

Prime factors of 58338 are 2, 3, 7, 463. Prime factorization of 58338 in exponential form is:

58338 = 2¹ × 3² × 7¹ × 463¹

Step-3: Factors of 58320

List of positive integer factors of 58320 that divides 58320 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

Step-4: Factors of 58338

List of positive integer factors of 58338 that divides 58320 without a remainder.

1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, 126, 463, 926, 1389, 2778, 3241, 4167, 6482, 8334, 9723, 19446, 29169

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 58320 and 58338. The biggest common factor number is the GCF number.
So the greatest common factor 58320 and 58338 is 18.

Also check out the Least Common Multiple of 58320 and 58338