What are the divisors of 3158?

1, 2, 1579, 3158

There is a total of 4 positive divisors.
The sum of these divisors is 4740.
The arithmetic mean is 1185.

2 even divisors

2, 3158

2 odd divisors

1, 1579

How to compute the divisors of 3158?

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 3158 by each of the numbers from 1 to 3158 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)

3158 / 1 = 3158 (the remainder is 0, so 1 is a divisor of 3158)
3158 / 2 = 1579 (the remainder is 0, so 2 is a divisor of 3158)
3158 / 3 = 1052.6666666667 (the remainder is 2, so 3 is not a divisor of 3158)
...
3158 / 3157 = 1.0003167564143 (the remainder is 1, so 3157 is not a divisor of 3158)
3158 / 3158 = 1 (the remainder is 0, so 3158 is a divisor of 3158)

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 3158 (i.e. 56.196085272908). 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 $\frac{N}{d} = D$ )

3158 / 1 = 3158 (the remainder is 0, so 1 and 3158 are divisors of 3158)
3158 / 2 = 1579 (the remainder is 0, so 2 and 1579 are divisors of 3158)
3158 / 3 = 1052.6666666667 (the remainder is 2, so 3 is not a divisor of 3158)
...
3158 / 55 = 57.418181818182 (the remainder is 23, so 55 is not a divisor of 3158)
3158 / 56 = 56.392857142857 (the remainder is 22, so 56 is not a divisor of 3158)