What is the Greatest Common Factor of 87200 and 87210?

Greatest common factor (GCF) of 87200 and 87210 is 10.

GCF(87200,87210) = 10

We will now calculate the prime factors of 87200 and 87210, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 87200 and 87210.

How to find the GCF of 87200 and 87210?

We will first find the prime factorization of 87200 and 87210. After we will calculate the factors of 87200 and 87210 and find the biggest common factor number .

Step-1: Prime Factorization of 87200

Prime factors of 87200 are 2, 5, 109. Prime factorization of 87200 in exponential form is:

87200 = 2⁵ × 5² × 109¹

Step-2: Prime Factorization of 87210

Prime factors of 87210 are 2, 3, 5, 17, 19. Prime factorization of 87210 in exponential form is:

87210 = 2¹ × 3³ × 5¹ × 17¹ × 19¹

Step-3: Factors of 87200

List of positive integer factors of 87200 that divides 87200 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 80, 100, 109, 160, 200, 218, 400, 436, 545, 800, 872, 1090, 1744, 2180, 2725, 3488, 4360, 5450, 8720, 10900, 17440, 21800, 43600

Step-4: Factors of 87210

List of positive integer factors of 87210 that divides 87200 without a remainder.

1, 2, 3, 5, 6, 9, 10, 15, 17, 18, 19, 27, 30, 34, 38, 45, 51, 54, 57, 85, 90, 95, 102, 114, 135, 153, 170, 171, 190, 255, 270, 285, 306, 323, 342, 459, 510, 513, 570, 646, 765, 855, 918, 969, 1026, 1530, 1615, 1710, 1938, 2295, 2565, 2907, 3230, 4590, 4845, 5130, 5814, 8721, 9690, 14535, 17442, 29070, 43605

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 87200 and 87210. The biggest common factor number is the GCF number.
So the greatest common factor 87200 and 87210 is 10.

Also check out the Least Common Multiple of 87200 and 87210