What is the Greatest Common Factor of 28200 and 28210?

Greatest common factor (GCF) of 28200 and 28210 is 10.

GCF(28200,28210) = 10

We will now calculate the prime factors of 28200 and 28210, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 28200 and 28210.

How to find the GCF of 28200 and 28210?

We will first find the prime factorization of 28200 and 28210. After we will calculate the factors of 28200 and 28210 and find the biggest common factor number .

Step-1: Prime Factorization of 28200

Prime factors of 28200 are 2, 3, 5, 47. Prime factorization of 28200 in exponential form is:

28200 = 2³ × 3¹ × 5² × 47¹

Step-2: Prime Factorization of 28210

Prime factors of 28210 are 2, 5, 7, 13, 31. Prime factorization of 28210 in exponential form is:

28210 = 2¹ × 5¹ × 7¹ × 13¹ × 31¹

Step-3: Factors of 28200

List of positive integer factors of 28200 that divides 28200 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 25, 30, 40, 47, 50, 60, 75, 94, 100, 120, 141, 150, 188, 200, 235, 282, 300, 376, 470, 564, 600, 705, 940, 1128, 1175, 1410, 1880, 2350, 2820, 3525, 4700, 5640, 7050, 9400, 14100

Step-4: Factors of 28210

List of positive integer factors of 28210 that divides 28200 without a remainder.

1, 2, 5, 7, 10, 13, 14, 26, 31, 35, 62, 65, 70, 91, 130, 155, 182, 217, 310, 403, 434, 455, 806, 910, 1085, 2015, 2170, 2821, 4030, 5642, 14105

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 28200 and 28210. The biggest common factor number is the GCF number.
So the greatest common factor 28200 and 28210 is 10.

Also check out the Least Common Multiple of 28200 and 28210