What is the Greatest Common Factor of 1014 and 1027?

Greatest common factor (GCF) of 1014 and 1027 is 13.

GCF(1014,1027) = 13

We will now calculate the prime factors of 1014 and 1027, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1014 and 1027.

How to find the GCF of 1014 and 1027?

We will first find the prime factorization of 1014 and 1027. After we will calculate the factors of 1014 and 1027 and find the biggest common factor number .

Step-1: Prime Factorization of 1014

Prime factors of 1014 are 2, 3, 13. Prime factorization of 1014 in exponential form is:

1014 = 2¹ × 3¹ × 13²

Step-2: Prime Factorization of 1027

Prime factors of 1027 are 13, 79. Prime factorization of 1027 in exponential form is:

1027 = 13¹ × 79¹

Step-3: Factors of 1014

List of positive integer factors of 1014 that divides 1014 without a remainder.

1, 2, 3, 6, 13, 26, 39, 78, 169, 338, 507

Step-4: Factors of 1027

List of positive integer factors of 1027 that divides 1014 without a remainder.

1, 13, 79

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1014 and 1027. The biggest common factor number is the GCF number.
So the greatest common factor 1014 and 1027 is 13.

Also check out the Least Common Multiple of 1014 and 1027