What are the divisors of 5162?

1, 2, 29, 58, 89, 178, 2581, 5162

There is a total of 8 positive divisors.
The sum of these divisors is 8100.
The arithmetic mean is 1012.5.

4 even divisors

2, 58, 178, 5162

4 odd divisors

1, 29, 89, 2581

How to compute the divisors of 5162?

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 5162 by each of the numbers from 1 to 5162 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)

5162 / 1 = 5162 (the remainder is 0, so 1 is a divisor of 5162)
5162 / 2 = 2581 (the remainder is 0, so 2 is a divisor of 5162)
5162 / 3 = 1720.6666666667 (the remainder is 2, so 3 is not a divisor of 5162)
...
5162 / 5161 = 1.0001937608991 (the remainder is 1, so 5161 is not a divisor of 5162)
5162 / 5162 = 1 (the remainder is 0, so 5162 is a divisor of 5162)

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 5162 (i.e. 71.847059786744). 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 $\frac{N}{d} = D$ )

5162 / 1 = 5162 (the remainder is 0, so 1 and 5162 are divisors of 5162)
5162 / 2 = 2581 (the remainder is 0, so 2 and 2581 are divisors of 5162)
5162 / 3 = 1720.6666666667 (the remainder is 2, so 3 is not a divisor of 5162)
...
5162 / 70 = 73.742857142857 (the remainder is 52, so 70 is not a divisor of 5162)
5162 / 71 = 72.704225352113 (the remainder is 50, so 71 is not a divisor of 5162)