What is the Greatest Common Factor of 58128 and 58140?

Greatest common factor (GCF) of 58128 and 58140 is 12.

GCF(58128,58140) = 12

We will now calculate the prime factors of 58128 and 58140, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 58128 and 58140.

How to find the GCF of 58128 and 58140?

We will first find the prime factorization of 58128 and 58140. After we will calculate the factors of 58128 and 58140 and find the biggest common factor number .

Step-1: Prime Factorization of 58128

Prime factors of 58128 are 2, 3, 7, 173. Prime factorization of 58128 in exponential form is:

58128 = 2⁴ × 3¹ × 7¹ × 173¹

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 58128

List of positive integer factors of 58128 that divides 58128 without a remainder.

1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 42, 48, 56, 84, 112, 168, 173, 336, 346, 519, 692, 1038, 1211, 1384, 2076, 2422, 2768, 3633, 4152, 4844, 7266, 8304, 9688, 14532, 19376, 29064

Step-4: Factors of 58140

List of positive integer factors of 58140 that divides 58128 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 58128 and 58140. The biggest common factor number is the GCF number.
So the greatest common factor 58128 and 58140 is 12.

Also check out the Least Common Multiple of 58128 and 58140