What is the Greatest Common Factor of 69185 and 69200?

Greatest common factor (GCF) of 69185 and 69200 is 5.

GCF(69185,69200) = 5

We will now calculate the prime factors of 69185 and 69200, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 69185 and 69200.

How to find the GCF of 69185 and 69200?

We will first find the prime factorization of 69185 and 69200. After we will calculate the factors of 69185 and 69200 and find the biggest common factor number .

Step-1: Prime Factorization of 69185

Prime factors of 69185 are 5, 101, 137. Prime factorization of 69185 in exponential form is:

69185 = 5¹ × 101¹ × 137¹

Step-2: Prime Factorization of 69200

Prime factors of 69200 are 2, 5, 173. Prime factorization of 69200 in exponential form is:

69200 = 2⁴ × 5² × 173¹

Step-3: Factors of 69185

List of positive integer factors of 69185 that divides 69185 without a remainder.

1, 5, 101, 137, 505, 685, 13837

Step-4: Factors of 69200

List of positive integer factors of 69200 that divides 69185 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 173, 200, 346, 400, 692, 865, 1384, 1730, 2768, 3460, 4325, 6920, 8650, 13840, 17300, 34600

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 69185 and 69200. The biggest common factor number is the GCF number.
So the greatest common factor 69185 and 69200 is 5.

Also check out the Least Common Multiple of 69185 and 69200