What are the divisors of 849?

1, 3, 283, 849

There is a total of 4 positive divisors.
The sum of these divisors is 1136.
The arithmetic mean is 284.

4 odd divisors

1, 3, 283, 849

How to compute the divisors of 849?

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 849 by each of the numbers from 1 to 849 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)

849 / 1 = 849 (the remainder is 0, so 1 is a divisor of 849)
849 / 2 = 424.5 (the remainder is 1, so 2 is not a divisor of 849)
849 / 3 = 283 (the remainder is 0, so 3 is a divisor of 849)
...
849 / 848 = 1.001179245283 (the remainder is 1, so 848 is not a divisor of 849)
849 / 849 = 1 (the remainder is 0, so 849 is a divisor of 849)

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 849 (i.e. 29.137604568667). 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 $\frac{N}{d} = D$ )

849 / 1 = 849 (the remainder is 0, so 1 and 849 are divisors of 849)
849 / 2 = 424.5 (the remainder is 1, so 2 is not a divisor of 849)
849 / 3 = 283 (the remainder is 0, so 3 and 283 are divisors of 849)
...
849 / 28 = 30.321428571429 (the remainder is 9, so 28 is not a divisor of 849)
849 / 29 = 29.275862068966 (the remainder is 8, so 29 is not a divisor of 849)