What is the Greatest Common Factor of 90200 and 90214?

Greatest common factor (GCF) of 90200 and 90214 is 2.

GCF(90200,90214) = 2

We will now calculate the prime factors of 90200 and 90214, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 90200 and 90214.

How to find the GCF of 90200 and 90214?

We will first find the prime factorization of 90200 and 90214. After we will calculate the factors of 90200 and 90214 and find the biggest common factor number .

Step-1: Prime Factorization of 90200

Prime factors of 90200 are 2, 5, 11, 41. Prime factorization of 90200 in exponential form is:

90200 = 2³ × 5² × 11¹ × 41¹

Step-2: Prime Factorization of 90214

Prime factors of 90214 are 2, 43, 1049. Prime factorization of 90214 in exponential form is:

90214 = 2¹ × 43¹ × 1049¹

Step-3: Factors of 90200

List of positive integer factors of 90200 that divides 90200 without a remainder.

1, 2, 4, 5, 8, 10, 11, 20, 22, 25, 40, 41, 44, 50, 55, 82, 88, 100, 110, 164, 200, 205, 220, 275, 328, 410, 440, 451, 550, 820, 902, 1025, 1100, 1640, 1804, 2050, 2200, 2255, 3608, 4100, 4510, 8200, 9020, 11275, 18040, 22550, 45100

Step-4: Factors of 90214

List of positive integer factors of 90214 that divides 90200 without a remainder.

1, 2, 43, 86, 1049, 2098, 45107

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 90200 and 90214. The biggest common factor number is the GCF number.
So the greatest common factor 90200 and 90214 is 2.

Also check out the Least Common Multiple of 90200 and 90214