What is the Greatest Common Factor of 16009 and 16016?

Greatest common factor (GCF) of 16009 and 16016 is 7.

GCF(16009,16016) = 7

We will now calculate the prime factors of 16009 and 16016, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 16009 and 16016.

How to find the GCF of 16009 and 16016?

We will first find the prime factorization of 16009 and 16016. After we will calculate the factors of 16009 and 16016 and find the biggest common factor number .

Step-1: Prime Factorization of 16009

Prime factors of 16009 are 7, 2287. Prime factorization of 16009 in exponential form is:

16009 = 7¹ × 2287¹

Step-2: Prime Factorization of 16016

Prime factors of 16016 are 2, 7, 11, 13. Prime factorization of 16016 in exponential form is:

16016 = 2⁴ × 7¹ × 11¹ × 13¹

Step-3: Factors of 16009

List of positive integer factors of 16009 that divides 16009 without a remainder.

1, 7, 2287

Step-4: Factors of 16016

List of positive integer factors of 16016 that divides 16009 without a remainder.

1, 2, 4, 7, 8, 11, 13, 14, 16, 22, 26, 28, 44, 52, 56, 77, 88, 91, 104, 112, 143, 154, 176, 182, 208, 286, 308, 364, 572, 616, 728, 1001, 1144, 1232, 1456, 2002, 2288, 4004, 8008

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 16009 and 16016. The biggest common factor number is the GCF number.
So the greatest common factor 16009 and 16016 is 7.

Also check out the Least Common Multiple of 16009 and 16016