What is the Greatest Common Factor of 89200 and 89205?

Greatest common factor (GCF) of 89200 and 89205 is 5.

GCF(89200,89205) = 5

We will now calculate the prime factors of 89200 and 89205, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 89200 and 89205.

How to find the GCF of 89200 and 89205?

We will first find the prime factorization of 89200 and 89205. After we will calculate the factors of 89200 and 89205 and find the biggest common factor number .

Step-1: Prime Factorization of 89200

Prime factors of 89200 are 2, 5, 223. Prime factorization of 89200 in exponential form is:

89200 = 2⁴ × 5² × 223¹

Step-2: Prime Factorization of 89205

Prime factors of 89205 are 3, 5, 19, 313. Prime factorization of 89205 in exponential form is:

89205 = 3¹ × 5¹ × 19¹ × 313¹

Step-3: Factors of 89200

List of positive integer factors of 89200 that divides 89200 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 200, 223, 400, 446, 892, 1115, 1784, 2230, 3568, 4460, 5575, 8920, 11150, 17840, 22300, 44600

Step-4: Factors of 89205

List of positive integer factors of 89205 that divides 89200 without a remainder.

1, 3, 5, 15, 19, 57, 95, 285, 313, 939, 1565, 4695, 5947, 17841, 29735

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 89200 and 89205. The biggest common factor number is the GCF number.
So the greatest common factor 89200 and 89205 is 5.

Also check out the Least Common Multiple of 89200 and 89205