What are the divisors of 4090?

1, 2, 5, 10, 409, 818, 2045, 4090

There is a total of 8 positive divisors.
The sum of these divisors is 7380.
The arithmetic mean is 922.5.

4 even divisors

2, 10, 818, 4090

4 odd divisors

1, 5, 409, 2045

How to compute the divisors of 4090?

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 4090 by each of the numbers from 1 to 4090 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)

4090 / 1 = 4090 (the remainder is 0, so 1 is a divisor of 4090)
4090 / 2 = 2045 (the remainder is 0, so 2 is a divisor of 4090)
4090 / 3 = 1363.3333333333 (the remainder is 1, so 3 is not a divisor of 4090)
...
4090 / 4089 = 1.0002445585718 (the remainder is 1, so 4089 is not a divisor of 4090)
4090 / 4090 = 1 (the remainder is 0, so 4090 is a divisor of 4090)

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 4090 (i.e. 63.953107821278). 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 $\frac{N}{d} = D$ )

4090 / 1 = 4090 (the remainder is 0, so 1 and 4090 are divisors of 4090)
4090 / 2 = 2045 (the remainder is 0, so 2 and 2045 are divisors of 4090)
4090 / 3 = 1363.3333333333 (the remainder is 1, so 3 is not a divisor of 4090)
...
4090 / 62 = 65.967741935484 (the remainder is 60, so 62 is not a divisor of 4090)
4090 / 63 = 64.920634920635 (the remainder is 58, so 63 is not a divisor of 4090)