What is the Greatest Common Factor of 1014 and 1029?

Greatest common factor (GCF) of 1014 and 1029 is 3.

GCF(1014,1029) = 3

We will now calculate the prime factors of 1014 and 1029, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1014 and 1029.

How to find the GCF of 1014 and 1029?

We will first find the prime factorization of 1014 and 1029. After we will calculate the factors of 1014 and 1029 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 1029

Prime factors of 1029 are 3, 7. Prime factorization of 1029 in exponential form is:

1029 = 3¹ × 7³

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 1029

List of positive integer factors of 1029 that divides 1014 without a remainder.

1, 3, 7, 21, 49, 147, 343

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1014 and 1029. The biggest common factor number is the GCF number.
So the greatest common factor 1014 and 1029 is 3.

Also check out the Least Common Multiple of 1014 and 1029