What is the sum of the distinct prime factors of 2016?
The prime factorization of 2016 is $2^5\cdot 3^2\cdot 7$. The distinct prime factors are 2, 3, and 7. Their sum is $2+3+7=\boxed{12}$.
To find the sum of the distinct prime factors of 2016, we first need to find the prime factorization of 2016.
The prime factorization of 2016 can be calculated by dividing it by the smallest prime number, which is 2, and continuing to divide the quotient by the smallest prime until the quotient is 1.
1. Divide 2016 by 2: 2016 ÷ 2 = 1008
2. Divide 1008 by 2: 1008 ÷ 2 = 504
3. Divide 504 by 2: 504 ÷ 2 = 252
4. Divide 252 by 2: 252 ÷ 2 = 126
5. Divide 126 by 2: 126 ÷ 2 = 63
6. 63 is not divisible by 2, so we move to the next prime number, which is 3.
7. Divide 63 by 3: 63 ÷ 3 = 21
8. 21 is not divisible by 3, so we move to the next prime number, which is 5.
9. Divide 21 by 5: 21 ÷ 5 = 4 remainder 1
10. 4 is divisible by 2: 4 ÷ 2 = 2
The prime factorization of 2016 is 2^5 × 3^2 × 7.
Now, we can find the sum of the distinct prime factors, which are 2, 3, and 7:
Sum = 2 + 3 + 7 = 12
Therefore, the sum of the distinct prime factors of 2016 is 12.