What are the divisors of 4004?

1, 2, 4, 7, 11, 13, 14, 22, 26, 28, 44, 52, 77, 91, 143, 154, 182, 286, 308, 364, 572, 1001, 2002, 4004

There is a total of 24 positive divisors.
The sum of these divisors is 9408.
The arithmetic mean is 392.

16 even divisors

2, 4, 14, 22, 26, 28, 44, 52, 154, 182, 286, 308, 364, 572, 2002, 4004

8 odd divisors

1, 7, 11, 13, 77, 91, 143, 1001

How to compute the divisors of 4004?

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 4004 by each of the numbers from 1 to 4004 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)

4004 / 1 = 4004 (the remainder is 0, so 1 is a divisor of 4004)
4004 / 2 = 2002 (the remainder is 0, so 2 is a divisor of 4004)
4004 / 3 = 1334.6666666667 (the remainder is 2, so 3 is not a divisor of 4004)
...
4004 / 4003 = 1.0002498126405 (the remainder is 1, so 4003 is not a divisor of 4004)
4004 / 4004 = 1 (the remainder is 0, so 4004 is a divisor of 4004)

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 4004 (i.e. 63.277168078226). 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 $\frac{N}{d} = D$ )

4004 / 1 = 4004 (the remainder is 0, so 1 and 4004 are divisors of 4004)
4004 / 2 = 2002 (the remainder is 0, so 2 and 2002 are divisors of 4004)
4004 / 3 = 1334.6666666667 (the remainder is 2, so 3 is not a divisor of 4004)
...
4004 / 62 = 64.58064516129 (the remainder is 36, so 62 is not a divisor of 4004)
4004 / 63 = 63.555555555556 (the remainder is 35, so 63 is not a divisor of 4004)