What is the Greatest Common Factor of 1998 and 2014?

Greatest common factor (GCF) of 1998 and 2014 is 2.

GCF(1998,2014) = 2

We will now calculate the prime factors of 1998 and 2014, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1998 and 2014.

How to find the GCF of 1998 and 2014?

We will first find the prime factorization of 1998 and 2014. After we will calculate the factors of 1998 and 2014 and find the biggest common factor number .

Step-1: Prime Factorization of 1998

Prime factors of 1998 are 2, 3, 37. Prime factorization of 1998 in exponential form is:

1998 = 2¹ × 3³ × 37¹

Step-2: 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-3: Factors of 1998

List of positive integer factors of 1998 that divides 1998 without a remainder.

1, 2, 3, 6, 9, 18, 27, 37, 54, 74, 111, 222, 333, 666, 999

Step-4: Factors of 2014

List of positive integer factors of 2014 that divides 1998 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1998 and 2014. The biggest common factor number is the GCF number.
So the greatest common factor 1998 and 2014 is 2.

Also check out the Least Common Multiple of 1998 and 2014