What is the Greatest Common Factor of 1314 and 1320?

Greatest common factor (GCF) of 1314 and 1320 is 6.

GCF(1314,1320) = 6

We will now calculate the prime factors of 1314 and 1320, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1314 and 1320.

How to find the GCF of 1314 and 1320?

We will first find the prime factorization of 1314 and 1320. After we will calculate the factors of 1314 and 1320 and find the biggest common factor number .

Step-1: Prime Factorization of 1314

Prime factors of 1314 are 2, 3, 73. Prime factorization of 1314 in exponential form is:

1314 = 2¹ × 3² × 73¹

Step-2: Prime Factorization of 1320

Prime factors of 1320 are 2, 3, 5, 11. Prime factorization of 1320 in exponential form is:

1320 = 2³ × 3¹ × 5¹ × 11¹

Step-3: Factors of 1314

List of positive integer factors of 1314 that divides 1314 without a remainder.

1, 2, 3, 6, 9, 18, 73, 146, 219, 438, 657

Step-4: Factors of 1320

List of positive integer factors of 1320 that divides 1314 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 11, 12, 15, 20, 22, 24, 30, 33, 40, 44, 55, 60, 66, 88, 110, 120, 132, 165, 220, 264, 330, 440, 660

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1314 and 1320. The biggest common factor number is the GCF number.
So the greatest common factor 1314 and 1320 is 6.

Also check out the Least Common Multiple of 1314 and 1320