What is the Greatest Common Factor of 7184 and 7200?

Greatest common factor (GCF) of 7184 and 7200 is 16.

GCF(7184,7200) = 16

We will now calculate the prime factors of 7184 and 7200, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 7184 and 7200.

How to find the GCF of 7184 and 7200?

We will first find the prime factorization of 7184 and 7200. After we will calculate the factors of 7184 and 7200 and find the biggest common factor number .

Step-1: Prime Factorization of 7184

Prime factors of 7184 are 2, 449. Prime factorization of 7184 in exponential form is:

7184 = 2⁴ × 449¹

Step-2: Prime Factorization of 7200

Prime factors of 7200 are 2, 3, 5. Prime factorization of 7200 in exponential form is:

7200 = 2⁵ × 3² × 5²

Step-3: Factors of 7184

List of positive integer factors of 7184 that divides 7184 without a remainder.

1, 2, 4, 8, 16, 449, 898, 1796, 3592

Step-4: Factors of 7200

List of positive integer factors of 7200 that divides 7184 without a remainder.

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 25, 30, 32, 36, 40, 45, 48, 50, 60, 72, 75, 80, 90, 96, 100, 120, 144, 150, 160, 180, 200, 225, 240, 288, 300, 360, 400, 450, 480, 600, 720, 800, 900, 1200, 1440, 1800, 2400, 3600

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 7184 and 7200. The biggest common factor number is the GCF number.
So the greatest common factor 7184 and 7200 is 16.

Also check out the Least Common Multiple of 7184 and 7200