What are the divisors of 879?

1, 3, 293, 879

There is a total of 4 positive divisors.
The sum of these divisors is 1176.
The arithmetic mean is 294.

4 odd divisors

1, 3, 293, 879

How to compute the divisors of 879?

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 879 by each of the numbers from 1 to 879 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)

879 / 1 = 879 (the remainder is 0, so 1 is a divisor of 879)
879 / 2 = 439.5 (the remainder is 1, so 2 is not a divisor of 879)
879 / 3 = 293 (the remainder is 0, so 3 is a divisor of 879)
...
879 / 878 = 1.001138952164 (the remainder is 1, so 878 is not a divisor of 879)
879 / 879 = 1 (the remainder is 0, so 879 is a divisor of 879)

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 879 (i.e. 29.647934160747). 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 $\frac{N}{d} = D$ )

879 / 1 = 879 (the remainder is 0, so 1 and 879 are divisors of 879)
879 / 2 = 439.5 (the remainder is 1, so 2 is not a divisor of 879)
879 / 3 = 293 (the remainder is 0, so 3 and 293 are divisors of 879)
...
879 / 28 = 31.392857142857 (the remainder is 11, so 28 is not a divisor of 879)
879 / 29 = 30.310344827586 (the remainder is 9, so 29 is not a divisor of 879)