What is the Greatest Common Factor of 69184 and 69200?

Greatest common factor (GCF) of 69184 and 69200 is 16.

GCF(69184,69200) = 16

We will now calculate the prime factors of 69184 and 69200, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 69184 and 69200.

How to find the GCF of 69184 and 69200?

We will first find the prime factorization of 69184 and 69200. After we will calculate the factors of 69184 and 69200 and find the biggest common factor number .

Step-1: Prime Factorization of 69184

Prime factors of 69184 are 2, 23, 47. Prime factorization of 69184 in exponential form is:

69184 = 2⁶ × 23¹ × 47¹

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 69184

List of positive integer factors of 69184 that divides 69184 without a remainder.

1, 2, 4, 8, 16, 23, 32, 46, 47, 64, 92, 94, 184, 188, 368, 376, 736, 752, 1081, 1472, 1504, 2162, 3008, 4324, 8648, 17296, 34592

Step-4: Factors of 69200

List of positive integer factors of 69200 that divides 69184 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 69184 and 69200. The biggest common factor number is the GCF number.
So the greatest common factor 69184 and 69200 is 16.

Also check out the Least Common Multiple of 69184 and 69200