What is the Greatest Common Factor of 2014 and 2028?

Greatest common factor (GCF) of 2014 and 2028 is 2.

GCF(2014,2028) = 2

We will now calculate the prime factors of 2014 and 2028, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 2014 and 2028.

How to find the GCF of 2014 and 2028?

We will first find the prime factorization of 2014 and 2028. After we will calculate the factors of 2014 and 2028 and find the biggest common factor number .

Step-1: Prime Factorization of 2014

Prime factors of 2014 are 2, 19, 53. Prime factorization of 2014 in exponential form is:

2014 = 2¹ × 19¹ × 53¹

Step-2: Prime Factorization of 2028

Prime factors of 2028 are 2, 3, 13. Prime factorization of 2028 in exponential form is:

2028 = 2² × 3¹ × 13²

Step-3: Factors of 2014

List of positive integer factors of 2014 that divides 2014 without a remainder.

1, 2, 19, 38, 53, 106, 1007

Step-4: Factors of 2028

List of positive integer factors of 2028 that divides 2014 without a remainder.

1, 2, 3, 4, 6, 12, 13, 26, 39, 52, 78, 156, 169, 338, 507, 676, 1014

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 2014 and 2028. The biggest common factor number is the GCF number.
So the greatest common factor 2014 and 2028 is 2.

Also check out the Least Common Multiple of 2014 and 2028