What is the Greatest Common Factor of 58125 and 58140?

Greatest common factor (GCF) of 58125 and 58140 is 15.

GCF(58125,58140) = 15

We will now calculate the prime factors of 58125 and 58140, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 58125 and 58140.

How to find the GCF of 58125 and 58140?

We will first find the prime factorization of 58125 and 58140. After we will calculate the factors of 58125 and 58140 and find the biggest common factor number .

Step-1: Prime Factorization of 58125

Prime factors of 58125 are 3, 5, 31. Prime factorization of 58125 in exponential form is:

58125 = 3¹ × 5⁴ × 31¹

Step-2: Prime Factorization of 58140

Prime factors of 58140 are 2, 3, 5, 17, 19. Prime factorization of 58140 in exponential form is:

58140 = 2² × 3² × 5¹ × 17¹ × 19¹

Step-3: Factors of 58125

List of positive integer factors of 58125 that divides 58125 without a remainder.

1, 3, 5, 15, 25, 31, 75, 93, 125, 155, 375, 465, 625, 775, 1875, 2325, 3875, 11625, 19375

Step-4: Factors of 58140

List of positive integer factors of 58140 that divides 58125 without a remainder.

1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 17, 18, 19, 20, 30, 34, 36, 38, 45, 51, 57, 60, 68, 76, 85, 90, 95, 102, 114, 153, 170, 171, 180, 190, 204, 228, 255, 285, 306, 323, 340, 342, 380, 510, 570, 612, 646, 684, 765, 855, 969, 1020, 1140, 1292, 1530, 1615, 1710, 1938, 2907, 3060, 3230, 3420, 3876, 4845, 5814, 6460, 9690, 11628, 14535, 19380, 29070

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 58125 and 58140. The biggest common factor number is the GCF number.
So the greatest common factor 58125 and 58140 is 15.

Also check out the Least Common Multiple of 58125 and 58140