What are the divisors of 2134?

1, 2, 11, 22, 97, 194, 1067, 2134

There is a total of 8 positive divisors.
The sum of these divisors is 3528.
The arithmetic mean is 441.

4 even divisors

2, 22, 194, 2134

4 odd divisors

1, 11, 97, 1067

How to compute the divisors of 2134?

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 2134 by each of the numbers from 1 to 2134 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)

2134 / 1 = 2134 (the remainder is 0, so 1 is a divisor of 2134)
2134 / 2 = 1067 (the remainder is 0, so 2 is a divisor of 2134)
2134 / 3 = 711.33333333333 (the remainder is 1, so 3 is not a divisor of 2134)
...
2134 / 2133 = 1.0004688232536 (the remainder is 1, so 2133 is not a divisor of 2134)
2134 / 2134 = 1 (the remainder is 0, so 2134 is a divisor of 2134)

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 2134 (i.e. 46.195237849804). 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 $\frac{N}{d} = D$ )

2134 / 1 = 2134 (the remainder is 0, so 1 and 2134 are divisors of 2134)
2134 / 2 = 1067 (the remainder is 0, so 2 and 1067 are divisors of 2134)
2134 / 3 = 711.33333333333 (the remainder is 1, so 3 is not a divisor of 2134)
...
2134 / 45 = 47.422222222222 (the remainder is 19, so 45 is not a divisor of 2134)
2134 / 46 = 46.391304347826 (the remainder is 18, so 46 is not a divisor of 2134)