What is the Greatest Common Factor of 58500 and 58520?

Greatest common factor (GCF) of 58500 and 58520 is 20.

GCF(58500,58520) = 20

We will now calculate the prime factors of 58500 and 58520, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 58500 and 58520.

How to find the GCF of 58500 and 58520?

We will first find the prime factorization of 58500 and 58520. After we will calculate the factors of 58500 and 58520 and find the biggest common factor number .

Step-1: Prime Factorization of 58500

Prime factors of 58500 are 2, 3, 5, 13. Prime factorization of 58500 in exponential form is:

58500 = 2² × 3² × 5³ × 13¹

Step-2: Prime Factorization of 58520

Prime factors of 58520 are 2, 5, 7, 11, 19. Prime factorization of 58520 in exponential form is:

58520 = 2³ × 5¹ × 7¹ × 11¹ × 19¹

Step-3: Factors of 58500

List of positive integer factors of 58500 that divides 58500 without a remainder.

1, 2, 3, 4, 5, 6, 9, 10, 12, 13, 15, 18, 20, 25, 26, 30, 36, 39, 45, 50, 52, 60, 65, 75, 78, 90, 100, 117, 125, 130, 150, 156, 180, 195, 225, 234, 250, 260, 300, 325, 375, 390, 450, 468, 500, 585, 650, 750, 780, 900, 975, 1125, 1170, 1300, 1500, 1625, 1950, 2250, 2340, 2925, 3250, 3900, 4500, 4875, 5850, 6500, 9750, 11700, 14625, 19500, 29250

Step-4: Factors of 58520

List of positive integer factors of 58520 that divides 58500 without a remainder.

1, 2, 4, 5, 7, 8, 10, 11, 14, 19, 20, 22, 28, 35, 38, 40, 44, 55, 56, 70, 76, 77, 88, 95, 110, 133, 140, 152, 154, 190, 209, 220, 266, 280, 308, 380, 385, 418, 440, 532, 616, 665, 760, 770, 836, 1045, 1064, 1330, 1463, 1540, 1672, 2090, 2660, 2926, 3080, 4180, 5320, 5852, 7315, 8360, 11704, 14630, 29260

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 58500 and 58520. The biggest common factor number is the GCF number.
So the greatest common factor 58500 and 58520 is 20.

Also check out the Least Common Multiple of 58500 and 58520