What are the divisors of 881?

1, 881

There is a total of 2 positive divisors.
The sum of these divisors is 882.
The arithmetic mean is 441.

2 odd divisors

1, 881

How to compute the divisors of 881?

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 881 by each of the numbers from 1 to 881 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)

881 / 1 = 881 (the remainder is 0, so 1 is a divisor of 881)
881 / 2 = 440.5 (the remainder is 1, so 2 is not a divisor of 881)
881 / 3 = 293.66666666667 (the remainder is 2, so 3 is not a divisor of 881)
...
881 / 880 = 1.0011363636364 (the remainder is 1, so 880 is not a divisor of 881)
881 / 881 = 1 (the remainder is 0, so 881 is a divisor of 881)

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 881 (i.e. 29.681644159312). 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 $\frac{N}{d} = D$ )

881 / 1 = 881 (the remainder is 0, so 1 and 881 are divisors of 881)
881 / 2 = 440.5 (the remainder is 1, so 2 is not a divisor of 881)
881 / 3 = 293.66666666667 (the remainder is 2, so 3 is not a divisor of 881)
...
881 / 28 = 31.464285714286 (the remainder is 13, so 28 is not a divisor of 881)
881 / 29 = 30.379310344828 (the remainder is 11, so 29 is not a divisor of 881)