What is the Greatest Common Factor of 13200 and 13214?

Greatest common factor (GCF) of 13200 and 13214 is 2.

GCF(13200,13214) = 2

We will now calculate the prime factors of 13200 and 13214, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13200 and 13214.

How to find the GCF of 13200 and 13214?

We will first find the prime factorization of 13200 and 13214. After we will calculate the factors of 13200 and 13214 and find the biggest common factor number .

Step-1: Prime Factorization of 13200

Prime factors of 13200 are 2, 3, 5, 11. Prime factorization of 13200 in exponential form is:

13200 = 2⁴ × 3¹ × 5² × 11¹

Step-2: Prime Factorization of 13214

Prime factors of 13214 are 2, 6607. Prime factorization of 13214 in exponential form is:

13214 = 2¹ × 6607¹

Step-3: Factors of 13200

List of positive integer factors of 13200 that divides 13200 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 11, 12, 15, 16, 20, 22, 24, 25, 30, 33, 40, 44, 48, 50, 55, 60, 66, 75, 80, 88, 100, 110, 120, 132, 150, 165, 176, 200, 220, 240, 264, 275, 300, 330, 400, 440, 528, 550, 600, 660, 825, 880, 1100, 1200, 1320, 1650, 2200, 2640, 3300, 4400, 6600

Step-4: Factors of 13214

List of positive integer factors of 13214 that divides 13200 without a remainder.

1, 2, 6607

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 13200 and 13214. The biggest common factor number is the GCF number.
So the greatest common factor 13200 and 13214 is 2.

Also check out the Least Common Multiple of 13200 and 13214