What is the Greatest Common Factor of 69200 and 69219?

Greatest common factor (GCF) of 69200 and 69219 is 1.

GCF(69200,69219) = 1

We will now calculate the prime factors of 69200 and 69219, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 69200 and 69219.

How to find the GCF of 69200 and 69219?

We will first find the prime factorization of 69200 and 69219. After we will calculate the factors of 69200 and 69219 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 69219

Prime factors of 69219 are 3, 7691. Prime factorization of 69219 in exponential form is:

69219 = 3² × 7691¹

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 69219

List of positive integer factors of 69219 that divides 69200 without a remainder.

1, 3, 9, 7691, 23073

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 69200 and 69219. The biggest common factor number is the GCF number.
So the greatest common factor 69200 and 69219 is 1.

Also check out the Least Common Multiple of 69200 and 69219