What is the Greatest Common Factor of 1314 and 1330?

Greatest common factor (GCF) of 1314 and 1330 is 2.

GCF(1314,1330) = 2

We will now calculate the prime factors of 1314 and 1330, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1314 and 1330.

How to find the GCF of 1314 and 1330?

We will first find the prime factorization of 1314 and 1330. After we will calculate the factors of 1314 and 1330 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 1330

Prime factors of 1330 are 2, 5, 7, 19. Prime factorization of 1330 in exponential form is:

1330 = 2¹ × 5¹ × 7¹ × 19¹

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 1330

List of positive integer factors of 1330 that divides 1314 without a remainder.

1, 2, 5, 7, 10, 14, 19, 35, 38, 70, 95, 133, 190, 266, 665

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1314 and 1330. The biggest common factor number is the GCF number.
So the greatest common factor 1314 and 1330 is 2.

Also check out the Least Common Multiple of 1314 and 1330