What are the divisors of 4016?

1, 2, 4, 8, 16, 251, 502, 1004, 2008, 4016

There is a total of 10 positive divisors.
The sum of these divisors is 7812.
The arithmetic mean is 781.2.

8 even divisors

2, 4, 8, 16, 502, 1004, 2008, 4016

2 odd divisors

1, 251

How to compute the divisors of 4016?

A number N is said to be divisible by a number M (with M non-zero) if, when we divide N by M, the remainder of the division is zero.

$N mod M = 0$

Brute force algorithm

We could start by using a brute-force method which would involve dividing 4016 by each of the numbers from 1 to 4016 to determine which ones have a remainder equal to 0.

$Remainder = N - (M \times ⌊ \frac{N}{M} ⌋)$

(where $⌊ \frac{N}{M} ⌋$ is the integer part of the quotient)

4016 / 1 = 4016 (the remainder is 0, so 1 is a divisor of 4016)
4016 / 2 = 2008 (the remainder is 0, so 2 is a divisor of 4016)
4016 / 3 = 1338.6666666667 (the remainder is 2, so 3 is not a divisor of 4016)
...
4016 / 4015 = 1.0002490660025 (the remainder is 1, so 4015 is not a divisor of 4016)
4016 / 4016 = 1 (the remainder is 0, so 4016 is a divisor of 4016)

Improved algorithm using square-root

However, there is another slightly better approach that reduces the number of iterations by testing only integers less than or equal to the square root of 4016 (i.e. 63.371918071019). Indeed, if a number N has a divisor D greater than its square root, then there is necessarily a smaller divisor d such that:

$D \times d = N$

(thus, if $\frac{N}{D} = d$ , then $\frac{N}{d} = D$ )

4016 / 1 = 4016 (the remainder is 0, so 1 and 4016 are divisors of 4016)
4016 / 2 = 2008 (the remainder is 0, so 2 and 2008 are divisors of 4016)
4016 / 3 = 1338.6666666667 (the remainder is 2, so 3 is not a divisor of 4016)
...
4016 / 62 = 64.774193548387 (the remainder is 48, so 62 is not a divisor of 4016)
4016 / 63 = 63.746031746032 (the remainder is 47, so 63 is not a divisor of 4016)