What are the divisors of 4046?

1, 2, 7, 14, 17, 34, 119, 238, 289, 578, 2023, 4046

There is a total of 12 positive divisors.
The sum of these divisors is 7368.
The arithmetic mean is 614.

6 even divisors

2, 14, 34, 238, 578, 4046

6 odd divisors

1, 7, 17, 119, 289, 2023

How to compute the divisors of 4046?

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 4046 by each of the numbers from 1 to 4046 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)

4046 / 1 = 4046 (the remainder is 0, so 1 is a divisor of 4046)
4046 / 2 = 2023 (the remainder is 0, so 2 is a divisor of 4046)
4046 / 3 = 1348.6666666667 (the remainder is 2, so 3 is not a divisor of 4046)
...
4046 / 4045 = 1.0002472187886 (the remainder is 1, so 4045 is not a divisor of 4046)
4046 / 4046 = 1 (the remainder is 0, so 4046 is a divisor of 4046)

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 4046 (i.e. 63.608175575157). 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 $\frac{N}{d} = D$ )

4046 / 1 = 4046 (the remainder is 0, so 1 and 4046 are divisors of 4046)
4046 / 2 = 2023 (the remainder is 0, so 2 and 2023 are divisors of 4046)
4046 / 3 = 1348.6666666667 (the remainder is 2, so 3 is not a divisor of 4046)
...
4046 / 62 = 65.258064516129 (the remainder is 16, so 62 is not a divisor of 4046)
4046 / 63 = 64.222222222222 (the remainder is 14, so 63 is not a divisor of 4046)