What is the Greatest Common Factor of 1001 and 1014?

Greatest common factor (GCF) of 1001 and 1014 is 13.

GCF(1001,1014) = 13

We will now calculate the prime factors of 1001 and 1014, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1001 and 1014.

How to find the GCF of 1001 and 1014?

We will first find the prime factorization of 1001 and 1014. After we will calculate the factors of 1001 and 1014 and find the biggest common factor number .

Step-1: Prime Factorization of 1001

Prime factors of 1001 are 7, 11, 13. Prime factorization of 1001 in exponential form is:

1001 = 7¹ × 11¹ × 13¹

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 1001

List of positive integer factors of 1001 that divides 1001 without a remainder.

1, 7, 11, 13, 77, 91, 143

Step-4: Factors of 1014

List of positive integer factors of 1014 that divides 1001 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 1001 and 1014. The biggest common factor number is the GCF number.
So the greatest common factor 1001 and 1014 is 13.

Also check out the Least Common Multiple of 1001 and 1014