What are the divisors of 883?

1, 883

There is a total of 2 positive divisors.
The sum of these divisors is 884.
The arithmetic mean is 442.

2 odd divisors

1, 883

How to compute the divisors of 883?

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 883 by each of the numbers from 1 to 883 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)

883 / 1 = 883 (the remainder is 0, so 1 is a divisor of 883)
883 / 2 = 441.5 (the remainder is 1, so 2 is not a divisor of 883)
883 / 3 = 294.33333333333 (the remainder is 1, so 3 is not a divisor of 883)
...
883 / 882 = 1.0011337868481 (the remainder is 1, so 882 is not a divisor of 883)
883 / 883 = 1 (the remainder is 0, so 883 is a divisor of 883)

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 883 (i.e. 29.715315916207). 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 $\frac{N}{d} = D$ )

883 / 1 = 883 (the remainder is 0, so 1 and 883 are divisors of 883)
883 / 2 = 441.5 (the remainder is 1, so 2 is not a divisor of 883)
883 / 3 = 294.33333333333 (the remainder is 1, so 3 is not a divisor of 883)
...
883 / 28 = 31.535714285714 (the remainder is 15, so 28 is not a divisor of 883)
883 / 29 = 30.448275862069 (the remainder is 13, so 29 is not a divisor of 883)