What are the divisors of 839?

1, 839

There is a total of 2 positive divisors.
The sum of these divisors is 840.
The arithmetic mean is 420.

2 odd divisors

1, 839

How to compute the divisors of 839?

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 839 by each of the numbers from 1 to 839 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)

839 / 1 = 839 (the remainder is 0, so 1 is a divisor of 839)
839 / 2 = 419.5 (the remainder is 1, so 2 is not a divisor of 839)
839 / 3 = 279.66666666667 (the remainder is 2, so 3 is not a divisor of 839)
...
839 / 838 = 1.0011933174224 (the remainder is 1, so 838 is not a divisor of 839)
839 / 839 = 1 (the remainder is 0, so 839 is a divisor of 839)

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 839 (i.e. 28.96549671592). 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 $\frac{N}{d} = D$ )

839 / 1 = 839 (the remainder is 0, so 1 and 839 are divisors of 839)
839 / 2 = 419.5 (the remainder is 1, so 2 is not a divisor of 839)
839 / 3 = 279.66666666667 (the remainder is 2, so 3 is not a divisor of 839)
...
839 / 27 = 31.074074074074 (the remainder is 2, so 27 is not a divisor of 839)
839 / 28 = 29.964285714286 (the remainder is 27, so 28 is not a divisor of 839)