What are the divisors of 874?

1, 2, 19, 23, 38, 46, 437, 874

There is a total of 8 positive divisors.
The sum of these divisors is 1440.
The arithmetic mean is 180.

4 even divisors

2, 38, 46, 874

4 odd divisors

1, 19, 23, 437

How to compute the divisors of 874?

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 874 by each of the numbers from 1 to 874 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)

874 / 1 = 874 (the remainder is 0, so 1 is a divisor of 874)
874 / 2 = 437 (the remainder is 0, so 2 is a divisor of 874)
874 / 3 = 291.33333333333 (the remainder is 1, so 3 is not a divisor of 874)
...
874 / 873 = 1.0011454753723 (the remainder is 1, so 873 is not a divisor of 874)
874 / 874 = 1 (the remainder is 0, so 874 is a divisor of 874)

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 874 (i.e. 29.563490998189). 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 $\frac{N}{d} = D$ )

874 / 1 = 874 (the remainder is 0, so 1 and 874 are divisors of 874)
874 / 2 = 437 (the remainder is 0, so 2 and 437 are divisors of 874)
874 / 3 = 291.33333333333 (the remainder is 1, so 3 is not a divisor of 874)
...
874 / 28 = 31.214285714286 (the remainder is 6, so 28 is not a divisor of 874)
874 / 29 = 30.137931034483 (the remainder is 4, so 29 is not a divisor of 874)