What is the Greatest Common Factor of 2009 and 2016?

Greatest common factor (GCF) of 2009 and 2016 is 7.

GCF(2009,2016) = 7

We will now calculate the prime factors of 2009 and 2016, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 2009 and 2016.

How to find the GCF of 2009 and 2016?

We will first find the prime factorization of 2009 and 2016. After we will calculate the factors of 2009 and 2016 and find the biggest common factor number .

Step-1: Prime Factorization of 2009

Prime factors of 2009 are 7, 41. Prime factorization of 2009 in exponential form is:

2009 = 7² × 41¹

Step-2: 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-3: Factors of 2009

List of positive integer factors of 2009 that divides 2009 without a remainder.

1, 7, 41, 49, 287

Step-4: Factors of 2016

List of positive integer factors of 2016 that divides 2009 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 2009 and 2016. The biggest common factor number is the GCF number.
So the greatest common factor 2009 and 2016 is 7.

Also check out the Least Common Multiple of 2009 and 2016