What are the divisors of 893?

1, 19, 47, 893

There is a total of 4 positive divisors.
The sum of these divisors is 960.
The arithmetic mean is 240.

4 odd divisors

1, 19, 47, 893

How to compute the divisors of 893?

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 893 by each of the numbers from 1 to 893 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)

893 / 1 = 893 (the remainder is 0, so 1 is a divisor of 893)
893 / 2 = 446.5 (the remainder is 1, so 2 is not a divisor of 893)
893 / 3 = 297.66666666667 (the remainder is 2, so 3 is not a divisor of 893)
...
893 / 892 = 1.0011210762332 (the remainder is 1, so 892 is not a divisor of 893)
893 / 893 = 1 (the remainder is 0, so 893 is a divisor of 893)

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 893 (i.e. 29.883105594968). 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 $\frac{N}{d} = D$ )

893 / 1 = 893 (the remainder is 0, so 1 and 893 are divisors of 893)
893 / 2 = 446.5 (the remainder is 1, so 2 is not a divisor of 893)
893 / 3 = 297.66666666667 (the remainder is 2, so 3 is not a divisor of 893)
...
893 / 28 = 31.892857142857 (the remainder is 25, so 28 is not a divisor of 893)
893 / 29 = 30.793103448276 (the remainder is 23, so 29 is not a divisor of 893)