What are the divisors of 5161?

1, 13, 397, 5161

There is a total of 4 positive divisors.
The sum of these divisors is 5572.
The arithmetic mean is 1393.

4 odd divisors

1, 13, 397, 5161

How to compute the divisors of 5161?

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 5161 by each of the numbers from 1 to 5161 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)

5161 / 1 = 5161 (the remainder is 0, so 1 is a divisor of 5161)
5161 / 2 = 2580.5 (the remainder is 1, so 2 is not a divisor of 5161)
5161 / 3 = 1720.3333333333 (the remainder is 1, so 3 is not a divisor of 5161)
...
5161 / 5160 = 1.0001937984496 (the remainder is 1, so 5160 is not a divisor of 5161)
5161 / 5161 = 1 (the remainder is 0, so 5161 is a divisor of 5161)

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 5161 (i.e. 71.840100222647). 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 $\frac{N}{d} = D$ )

5161 / 1 = 5161 (the remainder is 0, so 1 and 5161 are divisors of 5161)
5161 / 2 = 2580.5 (the remainder is 1, so 2 is not a divisor of 5161)
5161 / 3 = 1720.3333333333 (the remainder is 1, so 3 is not a divisor of 5161)
...
5161 / 70 = 73.728571428571 (the remainder is 51, so 70 is not a divisor of 5161)
5161 / 71 = 72.69014084507 (the remainder is 49, so 71 is not a divisor of 5161)