What are the divisors of 878?

1, 2, 439, 878

There is a total of 4 positive divisors.
The sum of these divisors is 1320.
The arithmetic mean is 330.

2 even divisors

2, 878

2 odd divisors

1, 439

How to compute the divisors of 878?

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 878 by each of the numbers from 1 to 878 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)

878 / 1 = 878 (the remainder is 0, so 1 is a divisor of 878)
878 / 2 = 439 (the remainder is 0, so 2 is a divisor of 878)
878 / 3 = 292.66666666667 (the remainder is 2, so 3 is not a divisor of 878)
...
878 / 877 = 1.0011402508552 (the remainder is 1, so 877 is not a divisor of 878)
878 / 878 = 1 (the remainder is 0, so 878 is a divisor of 878)

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 878 (i.e. 29.631064780058). 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 $\frac{N}{d} = D$ )

878 / 1 = 878 (the remainder is 0, so 1 and 878 are divisors of 878)
878 / 2 = 439 (the remainder is 0, so 2 and 439 are divisors of 878)
878 / 3 = 292.66666666667 (the remainder is 2, so 3 is not a divisor of 878)
...
878 / 28 = 31.357142857143 (the remainder is 10, so 28 is not a divisor of 878)
878 / 29 = 30.275862068966 (the remainder is 8, so 29 is not a divisor of 878)