What are the divisors of 884?

1, 2, 4, 13, 17, 26, 34, 52, 68, 221, 442, 884

There is a total of 12 positive divisors.
The sum of these divisors is 1764.
The arithmetic mean is 147.

8 even divisors

2, 4, 26, 34, 52, 68, 442, 884

4 odd divisors

1, 13, 17, 221

How to compute the divisors of 884?

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 884 by each of the numbers from 1 to 884 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)

884 / 1 = 884 (the remainder is 0, so 1 is a divisor of 884)
884 / 2 = 442 (the remainder is 0, so 2 is a divisor of 884)
884 / 3 = 294.66666666667 (the remainder is 2, so 3 is not a divisor of 884)
...
884 / 883 = 1.0011325028313 (the remainder is 1, so 883 is not a divisor of 884)
884 / 884 = 1 (the remainder is 0, so 884 is a divisor of 884)

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 884 (i.e. 29.732137494637). 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 $\frac{N}{d} = D$ )

884 / 1 = 884 (the remainder is 0, so 1 and 884 are divisors of 884)
884 / 2 = 442 (the remainder is 0, so 2 and 442 are divisors of 884)
884 / 3 = 294.66666666667 (the remainder is 2, so 3 is not a divisor of 884)
...
884 / 28 = 31.571428571429 (the remainder is 16, so 28 is not a divisor of 884)
884 / 29 = 30.48275862069 (the remainder is 14, so 29 is not a divisor of 884)