What is the Greatest Common Factor of 7200 and 7218?

Greatest common factor (GCF) of 7200 and 7218 is 18.

GCF(7200,7218) = 18

We will now calculate the prime factors of 7200 and 7218, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 7200 and 7218.

How to find the GCF of 7200 and 7218?

We will first find the prime factorization of 7200 and 7218. After we will calculate the factors of 7200 and 7218 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 7218

Prime factors of 7218 are 2, 3, 401. Prime factorization of 7218 in exponential form is:

7218 = 2¹ × 3² × 401¹

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 7218

List of positive integer factors of 7218 that divides 7200 without a remainder.

1, 2, 3, 6, 9, 18, 401, 802, 1203, 2406, 3609

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 7200 and 7218. The biggest common factor number is the GCF number.
So the greatest common factor 7200 and 7218 is 18.

Also check out the Least Common Multiple of 7200 and 7218