What are the divisors of 4408?

1, 2, 4, 8, 19, 29, 38, 58, 76, 116, 152, 232, 551, 1102, 2204, 4408

There is a total of 16 positive divisors.
The sum of these divisors is 9000.
The arithmetic mean is 562.5.

12 even divisors

2, 4, 8, 38, 58, 76, 116, 152, 232, 1102, 2204, 4408

4 odd divisors

1, 19, 29, 551

How to compute the divisors of 4408?

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 4408 by each of the numbers from 1 to 4408 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)

4408 / 1 = 4408 (the remainder is 0, so 1 is a divisor of 4408)
4408 / 2 = 2204 (the remainder is 0, so 2 is a divisor of 4408)
4408 / 3 = 1469.3333333333 (the remainder is 1, so 3 is not a divisor of 4408)
...
4408 / 4407 = 1.0002269117313 (the remainder is 1, so 4407 is not a divisor of 4408)
4408 / 4408 = 1 (the remainder is 0, so 4408 is a divisor of 4408)

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 4408 (i.e. 66.392770690791). 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 $\frac{N}{d} = D$ )

4408 / 1 = 4408 (the remainder is 0, so 1 and 4408 are divisors of 4408)
4408 / 2 = 2204 (the remainder is 0, so 2 and 2204 are divisors of 4408)
4408 / 3 = 1469.3333333333 (the remainder is 1, so 3 is not a divisor of 4408)
...
4408 / 65 = 67.815384615385 (the remainder is 53, so 65 is not a divisor of 4408)
4408 / 66 = 66.787878787879 (the remainder is 52, so 66 is not a divisor of 4408)