What are the divisors of 3161?

1, 29, 109, 3161

There is a total of 4 positive divisors.
The sum of these divisors is 3300.
The arithmetic mean is 825.

4 odd divisors

1, 29, 109, 3161

How to compute the divisors of 3161?

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 3161 by each of the numbers from 1 to 3161 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)

3161 / 1 = 3161 (the remainder is 0, so 1 is a divisor of 3161)
3161 / 2 = 1580.5 (the remainder is 1, so 2 is not a divisor of 3161)
3161 / 3 = 1053.6666666667 (the remainder is 2, so 3 is not a divisor of 3161)
...
3161 / 3160 = 1.0003164556962 (the remainder is 1, so 3160 is not a divisor of 3161)
3161 / 3161 = 1 (the remainder is 0, so 3161 is a divisor of 3161)

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 3161 (i.e. 56.222771187482). 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 $\frac{N}{d} = D$ )

3161 / 1 = 3161 (the remainder is 0, so 1 and 3161 are divisors of 3161)
3161 / 2 = 1580.5 (the remainder is 1, so 2 is not a divisor of 3161)
3161 / 3 = 1053.6666666667 (the remainder is 2, so 3 is not a divisor of 3161)
...
3161 / 55 = 57.472727272727 (the remainder is 26, so 55 is not a divisor of 3161)
3161 / 56 = 56.446428571429 (the remainder is 25, so 56 is not a divisor of 3161)