What are the divisors of 5146?

1, 2, 31, 62, 83, 166, 2573, 5146

There is a total of 8 positive divisors.
The sum of these divisors is 8064.
The arithmetic mean is 1008.

4 even divisors

2, 62, 166, 5146

4 odd divisors

1, 31, 83, 2573

How to compute the divisors of 5146?

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 5146 by each of the numbers from 1 to 5146 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)

5146 / 1 = 5146 (the remainder is 0, so 1 is a divisor of 5146)
5146 / 2 = 2573 (the remainder is 0, so 2 is a divisor of 5146)
5146 / 3 = 1715.3333333333 (the remainder is 1, so 3 is not a divisor of 5146)
...
5146 / 5145 = 1.0001943634597 (the remainder is 1, so 5145 is not a divisor of 5146)
5146 / 5146 = 1 (the remainder is 0, so 5146 is a divisor of 5146)

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 5146 (i.e. 71.735625737844). 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 $\frac{N}{d} = D$ )

5146 / 1 = 5146 (the remainder is 0, so 1 and 5146 are divisors of 5146)
5146 / 2 = 2573 (the remainder is 0, so 2 and 2573 are divisors of 5146)
5146 / 3 = 1715.3333333333 (the remainder is 1, so 3 is not a divisor of 5146)
...
5146 / 70 = 73.514285714286 (the remainder is 36, so 70 is not a divisor of 5146)
5146 / 71 = 72.478873239437 (the remainder is 34, so 71 is not a divisor of 5146)