What are the divisors of 3134?

1, 2, 1567, 3134

There is a total of 4 positive divisors.
The sum of these divisors is 4704.
The arithmetic mean is 1176.

2 even divisors

2, 3134

2 odd divisors

1, 1567

How to compute the divisors of 3134?

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 3134 by each of the numbers from 1 to 3134 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)

3134 / 1 = 3134 (the remainder is 0, so 1 is a divisor of 3134)
3134 / 2 = 1567 (the remainder is 0, so 2 is a divisor of 3134)
3134 / 3 = 1044.6666666667 (the remainder is 2, so 3 is not a divisor of 3134)
...
3134 / 3133 = 1.0003191828918 (the remainder is 1, so 3133 is not a divisor of 3134)
3134 / 3134 = 1 (the remainder is 0, so 3134 is a divisor of 3134)

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 3134 (i.e. 55.982140009114). 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 $\frac{N}{d} = D$ )

3134 / 1 = 3134 (the remainder is 0, so 1 and 3134 are divisors of 3134)
3134 / 2 = 1567 (the remainder is 0, so 2 and 1567 are divisors of 3134)
3134 / 3 = 1044.6666666667 (the remainder is 2, so 3 is not a divisor of 3134)
...
3134 / 54 = 58.037037037037 (the remainder is 2, so 54 is not a divisor of 3134)
3134 / 55 = 56.981818181818 (the remainder is 54, so 55 is not a divisor of 3134)