What is the Greatest Common Factor of 2016 and 2034?

Greatest common factor (GCF) of 2016 and 2034 is 18.

GCF(2016,2034) = 18

We will now calculate the prime factors of 2016 and 2034, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 2016 and 2034.

How to find the GCF of 2016 and 2034?

We will first find the prime factorization of 2016 and 2034. After we will calculate the factors of 2016 and 2034 and find the biggest common factor number .

Step-1: Prime Factorization of 2016

Prime factors of 2016 are 2, 3, 7. Prime factorization of 2016 in exponential form is:

2016 = 2⁵ × 3² × 7¹

Step-2: Prime Factorization of 2034

Prime factors of 2034 are 2, 3, 113. Prime factorization of 2034 in exponential form is:

2034 = 2¹ × 3² × 113¹

Step-3: Factors of 2016

List of positive integer factors of 2016 that divides 2016 without a remainder.

1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 16, 18, 21, 24, 28, 32, 36, 42, 48, 56, 63, 72, 84, 96, 112, 126, 144, 168, 224, 252, 288, 336, 504, 672, 1008

Step-4: Factors of 2034

List of positive integer factors of 2034 that divides 2016 without a remainder.

1, 2, 3, 6, 9, 18, 113, 226, 339, 678, 1017

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 2016 and 2034. The biggest common factor number is the GCF number.
So the greatest common factor 2016 and 2034 is 18.

Also check out the Least Common Multiple of 2016 and 2034