What are the divisors of 4061?

1, 31, 131, 4061

There is a total of 4 positive divisors.
The sum of these divisors is 4224.
The arithmetic mean is 1056.

4 odd divisors

1, 31, 131, 4061

How to compute the divisors of 4061?

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 4061 by each of the numbers from 1 to 4061 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)

4061 / 1 = 4061 (the remainder is 0, so 1 is a divisor of 4061)
4061 / 2 = 2030.5 (the remainder is 1, so 2 is not a divisor of 4061)
4061 / 3 = 1353.6666666667 (the remainder is 2, so 3 is not a divisor of 4061)
...
4061 / 4060 = 1.0002463054187 (the remainder is 1, so 4060 is not a divisor of 4061)
4061 / 4061 = 1 (the remainder is 0, so 4061 is a divisor of 4061)

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 4061 (i.e. 63.725975865419). 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 $\frac{N}{d} = D$ )

4061 / 1 = 4061 (the remainder is 0, so 1 and 4061 are divisors of 4061)
4061 / 2 = 2030.5 (the remainder is 1, so 2 is not a divisor of 4061)
4061 / 3 = 1353.6666666667 (the remainder is 2, so 3 is not a divisor of 4061)
...
4061 / 62 = 65.5 (the remainder is 31, so 62 is not a divisor of 4061)
4061 / 63 = 64.460317460317 (the remainder is 29, so 63 is not a divisor of 4061)