What is the Greatest Common Factor of 1007 and 1014?

Greatest common factor (GCF) of 1007 and 1014 is 1.

GCF(1007,1014) = 1

We will now calculate the prime factors of 1007 and 1014, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1007 and 1014.

How to find the GCF of 1007 and 1014?

We will first find the prime factorization of 1007 and 1014. After we will calculate the factors of 1007 and 1014 and find the biggest common factor number .

Step-1: Prime Factorization of 1007

Prime factors of 1007 are 19, 53. Prime factorization of 1007 in exponential form is:

1007 = 19¹ × 53¹

Step-2: 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-3: Factors of 1007

List of positive integer factors of 1007 that divides 1007 without a remainder.

1, 19, 53

Step-4: Factors of 1014

List of positive integer factors of 1014 that divides 1007 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1007 and 1014. The biggest common factor number is the GCF number.
So the greatest common factor 1007 and 1014 is 1.

Also check out the Least Common Multiple of 1007 and 1014