What is the Greatest Common Factor of 58140 and 58160?

Greatest common factor (GCF) of 58140 and 58160 is 20.

GCF(58140,58160) = 20

We will now calculate the prime factors of 58140 and 58160, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 58140 and 58160.

How to find the GCF of 58140 and 58160?

We will first find the prime factorization of 58140 and 58160. After we will calculate the factors of 58140 and 58160 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 58160

Prime factors of 58160 are 2, 5, 727. Prime factorization of 58160 in exponential form is:

58160 = 2⁴ × 5¹ × 727¹

Step-3: Factors of 58140

List of positive integer factors of 58140 that divides 58140 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

Step-4: Factors of 58160

List of positive integer factors of 58160 that divides 58140 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 40, 80, 727, 1454, 2908, 3635, 5816, 7270, 11632, 14540, 29080

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 58140 and 58160. The biggest common factor number is the GCF number.
So the greatest common factor 58140 and 58160 is 20.

Also check out the Least Common Multiple of 58140 and 58160