What are the divisors of 847?

1, 7, 11, 77, 121, 847

There is a total of 6 positive divisors.
The sum of these divisors is 1064.
The arithmetic mean is 177.33333333333.

6 odd divisors

1, 7, 11, 77, 121, 847

How to compute the divisors of 847?

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 847 by each of the numbers from 1 to 847 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)

847 / 1 = 847 (the remainder is 0, so 1 is a divisor of 847)
847 / 2 = 423.5 (the remainder is 1, so 2 is not a divisor of 847)
847 / 3 = 282.33333333333 (the remainder is 1, so 3 is not a divisor of 847)
...
847 / 846 = 1.0011820330969 (the remainder is 1, so 846 is not a divisor of 847)
847 / 847 = 1 (the remainder is 0, so 847 is a divisor of 847)

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 847 (i.e. 29.10326442171). 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 $\frac{N}{d} = D$ )

847 / 1 = 847 (the remainder is 0, so 1 and 847 are divisors of 847)
847 / 2 = 423.5 (the remainder is 1, so 2 is not a divisor of 847)
847 / 3 = 282.33333333333 (the remainder is 1, so 3 is not a divisor of 847)
...
847 / 28 = 30.25 (the remainder is 7, so 28 is not a divisor of 847)
847 / 29 = 29.206896551724 (the remainder is 6, so 29 is not a divisor of 847)