What is the Greatest Common Factor of 16314 and 16320?

Greatest common factor (GCF) of 16314 and 16320 is 6.

GCF(16314,16320) = 6

We will now calculate the prime factors of 16314 and 16320, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 16314 and 16320.

How to find the GCF of 16314 and 16320?

We will first find the prime factorization of 16314 and 16320. After we will calculate the factors of 16314 and 16320 and find the biggest common factor number .

Step-1: Prime Factorization of 16314

Prime factors of 16314 are 2, 3, 2719. Prime factorization of 16314 in exponential form is:

16314 = 2¹ × 3¹ × 2719¹

Step-2: Prime Factorization of 16320

Prime factors of 16320 are 2, 3, 5, 17. Prime factorization of 16320 in exponential form is:

16320 = 2⁶ × 3¹ × 5¹ × 17¹

Step-3: Factors of 16314

List of positive integer factors of 16314 that divides 16314 without a remainder.

1, 2, 3, 6, 2719, 5438, 8157

Step-4: Factors of 16320

List of positive integer factors of 16320 that divides 16314 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 17, 20, 24, 30, 32, 34, 40, 48, 51, 60, 64, 68, 80, 85, 96, 102, 120, 136, 160, 170, 192, 204, 240, 255, 272, 320, 340, 408, 480, 510, 544, 680, 816, 960, 1020, 1088, 1360, 1632, 2040, 2720, 3264, 4080, 5440, 8160

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 16314 and 16320. The biggest common factor number is the GCF number.
So the greatest common factor 16314 and 16320 is 6.

Also check out the Least Common Multiple of 16314 and 16320