What is the Greatest Common Factor of 7200 and 7206?

Greatest common factor (GCF) of 7200 and 7206 is 6.

GCF(7200,7206) = 6

We will now calculate the prime factors of 7200 and 7206, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 7200 and 7206.

How to find the GCF of 7200 and 7206?

We will first find the prime factorization of 7200 and 7206. After we will calculate the factors of 7200 and 7206 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 7206

Prime factors of 7206 are 2, 3, 1201. Prime factorization of 7206 in exponential form is:

7206 = 2¹ × 3¹ × 1201¹

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 7206

List of positive integer factors of 7206 that divides 7200 without a remainder.

1, 2, 3, 6, 1201, 2402, 3603

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 7200 and 7206. The biggest common factor number is the GCF number.
So the greatest common factor 7200 and 7206 is 6.

Also check out the Least Common Multiple of 7200 and 7206