What is the Greatest Common Factor of 7200 and 7216?

Greatest common factor (GCF) of 7200 and 7216 is 16.

GCF(7200,7216) = 16

We will now calculate the prime factors of 7200 and 7216, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 7200 and 7216.

How to find the GCF of 7200 and 7216?

We will first find the prime factorization of 7200 and 7216. After we will calculate the factors of 7200 and 7216 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 7216

Prime factors of 7216 are 2, 11, 41. Prime factorization of 7216 in exponential form is:

7216 = 2⁴ × 11¹ × 41¹

Step-3: Factors of 7200

List of positive integer factors of 7200 that divides 7200 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

Step-4: Factors of 7216

List of positive integer factors of 7216 that divides 7200 without a remainder.

1, 2, 4, 8, 11, 16, 22, 41, 44, 82, 88, 164, 176, 328, 451, 656, 902, 1804, 3608

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 7200 and 7216. The biggest common factor number is the GCF number.
So the greatest common factor 7200 and 7216 is 16.

Also check out the Least Common Multiple of 7200 and 7216