What are the divisors of 4039?

1, 7, 577, 4039

There is a total of 4 positive divisors.
The sum of these divisors is 4624.
The arithmetic mean is 1156.

4 odd divisors

1, 7, 577, 4039

How to compute the divisors of 4039?

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 4039 by each of the numbers from 1 to 4039 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)

4039 / 1 = 4039 (the remainder is 0, so 1 is a divisor of 4039)
4039 / 2 = 2019.5 (the remainder is 1, so 2 is not a divisor of 4039)
4039 / 3 = 1346.3333333333 (the remainder is 1, so 3 is not a divisor of 4039)
...
4039 / 4038 = 1.0002476473502 (the remainder is 1, so 4038 is not a divisor of 4039)
4039 / 4039 = 1 (the remainder is 0, so 4039 is a divisor of 4039)

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 4039 (i.e. 63.553127381743). 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 $\frac{N}{d} = D$ )

4039 / 1 = 4039 (the remainder is 0, so 1 and 4039 are divisors of 4039)
4039 / 2 = 2019.5 (the remainder is 1, so 2 is not a divisor of 4039)
4039 / 3 = 1346.3333333333 (the remainder is 1, so 3 is not a divisor of 4039)
...
4039 / 62 = 65.145161290323 (the remainder is 9, so 62 is not a divisor of 4039)
4039 / 63 = 64.111111111111 (the remainder is 7, so 63 is not a divisor of 4039)