What are the divisors of 833?

1, 7, 17, 49, 119, 833

There is a total of 6 positive divisors.
The sum of these divisors is 1026.
The arithmetic mean is 171.

6 odd divisors

1, 7, 17, 49, 119, 833

How to compute the divisors of 833?

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 833 by each of the numbers from 1 to 833 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)

833 / 1 = 833 (the remainder is 0, so 1 is a divisor of 833)
833 / 2 = 416.5 (the remainder is 1, so 2 is not a divisor of 833)
833 / 3 = 277.66666666667 (the remainder is 2, so 3 is not a divisor of 833)
...
833 / 832 = 1.0012019230769 (the remainder is 1, so 832 is not a divisor of 833)
833 / 833 = 1 (the remainder is 0, so 833 is a divisor of 833)

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 833 (i.e. 28.861739379324). 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 $\frac{N}{d} = D$ )

833 / 1 = 833 (the remainder is 0, so 1 and 833 are divisors of 833)
833 / 2 = 416.5 (the remainder is 1, so 2 is not a divisor of 833)
833 / 3 = 277.66666666667 (the remainder is 2, so 3 is not a divisor of 833)
...
833 / 27 = 30.851851851852 (the remainder is 23, so 27 is not a divisor of 833)
833 / 28 = 29.75 (the remainder is 21, so 28 is not a divisor of 833)