What is the Greatest Common Factor of 7200 and 7208?

Greatest common factor (GCF) of 7200 and 7208 is 8.

GCF(7200,7208) = 8

We will now calculate the prime factors of 7200 and 7208, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 7200 and 7208.

How to find the GCF of 7200 and 7208?

We will first find the prime factorization of 7200 and 7208. After we will calculate the factors of 7200 and 7208 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 7208

Prime factors of 7208 are 2, 17, 53. Prime factorization of 7208 in exponential form is:

7208 = 2³ × 17¹ × 53¹

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 7208

List of positive integer factors of 7208 that divides 7200 without a remainder.

1, 2, 4, 8, 17, 34, 53, 68, 106, 136, 212, 424, 901, 1802, 3604

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 7200 and 7208. The biggest common factor number is the GCF number.
So the greatest common factor 7200 and 7208 is 8.

Also check out the Least Common Multiple of 7200 and 7208