What are the divisors of 5883?

1, 3, 37, 53, 111, 159, 1961, 5883

There is a total of 8 positive divisors.
The sum of these divisors is 8208.
The arithmetic mean is 1026.

8 odd divisors

1, 3, 37, 53, 111, 159, 1961, 5883

How to compute the divisors of 5883?

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 5883 by each of the numbers from 1 to 5883 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)

5883 / 1 = 5883 (the remainder is 0, so 1 is a divisor of 5883)
5883 / 2 = 2941.5 (the remainder is 1, so 2 is not a divisor of 5883)
5883 / 3 = 1961 (the remainder is 0, so 3 is a divisor of 5883)
...
5883 / 5882 = 1.0001700102006 (the remainder is 1, so 5882 is not a divisor of 5883)
5883 / 5883 = 1 (the remainder is 0, so 5883 is a divisor of 5883)

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 5883 (i.e. 76.700717076179). 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 $\frac{N}{d} = D$ )

5883 / 1 = 5883 (the remainder is 0, so 1 and 5883 are divisors of 5883)
5883 / 2 = 2941.5 (the remainder is 1, so 2 is not a divisor of 5883)
5883 / 3 = 1961 (the remainder is 0, so 3 and 1961 are divisors of 5883)
...
5883 / 75 = 78.44 (the remainder is 33, so 75 is not a divisor of 5883)
5883 / 76 = 77.407894736842 (the remainder is 31, so 76 is not a divisor of 5883)