What is the Greatest Common Factor of 69200 and 69205?

Greatest common factor (GCF) of 69200 and 69205 is 5.

GCF(69200,69205) = 5

We will now calculate the prime factors of 69200 and 69205, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 69200 and 69205.

How to find the GCF of 69200 and 69205?

We will first find the prime factorization of 69200 and 69205. After we will calculate the factors of 69200 and 69205 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 69205

Prime factors of 69205 are 5, 13841. Prime factorization of 69205 in exponential form is:

69205 = 5¹ × 13841¹

Step-3: Factors of 69200

List of positive integer factors of 69200 that divides 69200 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

Step-4: Factors of 69205

List of positive integer factors of 69205 that divides 69200 without a remainder.

1, 5, 13841

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 69200 and 69205. The biggest common factor number is the GCF number.
So the greatest common factor 69200 and 69205 is 5.

Also check out the Least Common Multiple of 69200 and 69205