What are the divisors of 880?

1, 2, 4, 5, 8, 10, 11, 16, 20, 22, 40, 44, 55, 80, 88, 110, 176, 220, 440, 880

There is a total of 20 positive divisors.
The sum of these divisors is 2232.
The arithmetic mean is 111.6.

16 even divisors

2, 4, 8, 10, 16, 20, 22, 40, 44, 80, 88, 110, 176, 220, 440, 880

4 odd divisors

1, 5, 11, 55

How to compute the divisors of 880?

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 880 by each of the numbers from 1 to 880 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)

880 / 1 = 880 (the remainder is 0, so 1 is a divisor of 880)
880 / 2 = 440 (the remainder is 0, so 2 is a divisor of 880)
880 / 3 = 293.33333333333 (the remainder is 1, so 3 is not a divisor of 880)
...
880 / 879 = 1.0011376564278 (the remainder is 1, so 879 is not a divisor of 880)
880 / 880 = 1 (the remainder is 0, so 880 is a divisor of 880)

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 880 (i.e. 29.664793948383). 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 $\frac{N}{d} = D$ )

880 / 1 = 880 (the remainder is 0, so 1 and 880 are divisors of 880)
880 / 2 = 440 (the remainder is 0, so 2 and 440 are divisors of 880)
880 / 3 = 293.33333333333 (the remainder is 1, so 3 is not a divisor of 880)
...
880 / 28 = 31.428571428571 (the remainder is 12, so 28 is not a divisor of 880)
880 / 29 = 30.344827586207 (the remainder is 10, so 29 is not a divisor of 880)