What is the Greatest Common Factor of 58576 and 58590?

Greatest common factor (GCF) of 58576 and 58590 is 14.

GCF(58576,58590) = 14

We will now calculate the prime factors of 58576 and 58590, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 58576 and 58590.

How to find the GCF of 58576 and 58590?

We will first find the prime factorization of 58576 and 58590. After we will calculate the factors of 58576 and 58590 and find the biggest common factor number .

Step-1: Prime Factorization of 58576

Prime factors of 58576 are 2, 7, 523. Prime factorization of 58576 in exponential form is:

58576 = 2⁴ × 7¹ × 523¹

Step-2: Prime Factorization of 58590

Prime factors of 58590 are 2, 3, 5, 7, 31. Prime factorization of 58590 in exponential form is:

58590 = 2¹ × 3³ × 5¹ × 7¹ × 31¹

Step-3: Factors of 58576

List of positive integer factors of 58576 that divides 58576 without a remainder.

1, 2, 4, 7, 8, 14, 16, 28, 56, 112, 523, 1046, 2092, 3661, 4184, 7322, 8368, 14644, 29288

Step-4: Factors of 58590

List of positive integer factors of 58590 that divides 58576 without a remainder.

1, 2, 3, 5, 6, 7, 9, 10, 14, 15, 18, 21, 27, 30, 31, 35, 42, 45, 54, 62, 63, 70, 90, 93, 105, 126, 135, 155, 186, 189, 210, 217, 270, 279, 310, 315, 378, 434, 465, 558, 630, 651, 837, 930, 945, 1085, 1302, 1395, 1674, 1890, 1953, 2170, 2790, 3255, 3906, 4185, 5859, 6510, 8370, 9765, 11718, 19530, 29295

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 58576 and 58590. The biggest common factor number is the GCF number.
So the greatest common factor 58576 and 58590 is 14.

Also check out the Least Common Multiple of 58576 and 58590