What are the divisors of 4404?

1, 2, 3, 4, 6, 12, 367, 734, 1101, 1468, 2202, 4404

There is a total of 12 positive divisors.
The sum of these divisors is 10304.
The arithmetic mean is 858.66666666667.

8 even divisors

2, 4, 6, 12, 734, 1468, 2202, 4404

4 odd divisors

1, 3, 367, 1101

How to compute the divisors of 4404?

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 4404 by each of the numbers from 1 to 4404 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)

4404 / 1 = 4404 (the remainder is 0, so 1 is a divisor of 4404)
4404 / 2 = 2202 (the remainder is 0, so 2 is a divisor of 4404)
4404 / 3 = 1468 (the remainder is 0, so 3 is a divisor of 4404)
...
4404 / 4403 = 1.0002271178742 (the remainder is 1, so 4403 is not a divisor of 4404)
4404 / 4404 = 1 (the remainder is 0, so 4404 is a divisor of 4404)

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 4404 (i.e. 66.362640092148). 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 $\frac{N}{d} = D$ )

4404 / 1 = 4404 (the remainder is 0, so 1 and 4404 are divisors of 4404)
4404 / 2 = 2202 (the remainder is 0, so 2 and 2202 are divisors of 4404)
4404 / 3 = 1468 (the remainder is 0, so 3 and 1468 are divisors of 4404)
...
4404 / 65 = 67.753846153846 (the remainder is 49, so 65 is not a divisor of 4404)
4404 / 66 = 66.727272727273 (the remainder is 48, so 66 is not a divisor of 4404)