What are the divisors of 889?

1, 7, 127, 889

There is a total of 4 positive divisors.
The sum of these divisors is 1024.
The arithmetic mean is 256.

4 odd divisors

1, 7, 127, 889

How to compute the divisors of 889?

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 889 by each of the numbers from 1 to 889 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)

889 / 1 = 889 (the remainder is 0, so 1 is a divisor of 889)
889 / 2 = 444.5 (the remainder is 1, so 2 is not a divisor of 889)
889 / 3 = 296.33333333333 (the remainder is 1, so 3 is not a divisor of 889)
...
889 / 888 = 1.0011261261261 (the remainder is 1, so 888 is not a divisor of 889)
889 / 889 = 1 (the remainder is 0, so 889 is a divisor of 889)

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 889 (i.e. 29.816103031751). 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 $\frac{N}{d} = D$ )

889 / 1 = 889 (the remainder is 0, so 1 and 889 are divisors of 889)
889 / 2 = 444.5 (the remainder is 1, so 2 is not a divisor of 889)
889 / 3 = 296.33333333333 (the remainder is 1, so 3 is not a divisor of 889)
...
889 / 28 = 31.75 (the remainder is 21, so 28 is not a divisor of 889)
889 / 29 = 30.655172413793 (the remainder is 19, so 29 is not a divisor of 889)