What are the divisors of 853?

1, 853

There is a total of 2 positive divisors.
The sum of these divisors is 854.
The arithmetic mean is 427.

2 odd divisors

1, 853

How to compute the divisors of 853?

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 853 by each of the numbers from 1 to 853 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)

853 / 1 = 853 (the remainder is 0, so 1 is a divisor of 853)
853 / 2 = 426.5 (the remainder is 1, so 2 is not a divisor of 853)
853 / 3 = 284.33333333333 (the remainder is 1, so 3 is not a divisor of 853)
...
853 / 852 = 1.0011737089202 (the remainder is 1, so 852 is not a divisor of 853)
853 / 853 = 1 (the remainder is 0, so 853 is a divisor of 853)

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 853 (i.e. 29.20616373302). 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 $\frac{N}{d} = D$ )

853 / 1 = 853 (the remainder is 0, so 1 and 853 are divisors of 853)
853 / 2 = 426.5 (the remainder is 1, so 2 is not a divisor of 853)
853 / 3 = 284.33333333333 (the remainder is 1, so 3 is not a divisor of 853)
...
853 / 28 = 30.464285714286 (the remainder is 13, so 28 is not a divisor of 853)
853 / 29 = 29.413793103448 (the remainder is 12, so 29 is not a divisor of 853)