What are the divisors of 899?

1, 29, 31, 899

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

4 odd divisors

1, 29, 31, 899

How to compute the divisors of 899?

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 899 by each of the numbers from 1 to 899 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)

899 / 1 = 899 (the remainder is 0, so 1 is a divisor of 899)
899 / 2 = 449.5 (the remainder is 1, so 2 is not a divisor of 899)
899 / 3 = 299.66666666667 (the remainder is 2, so 3 is not a divisor of 899)
...
899 / 898 = 1.0011135857461 (the remainder is 1, so 898 is not a divisor of 899)
899 / 899 = 1 (the remainder is 0, so 899 is a divisor of 899)

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 899 (i.e. 29.98332870113). 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 $\frac{N}{d} = D$ )

899 / 1 = 899 (the remainder is 0, so 1 and 899 are divisors of 899)
899 / 2 = 449.5 (the remainder is 1, so 2 is not a divisor of 899)
899 / 3 = 299.66666666667 (the remainder is 2, so 3 is not a divisor of 899)
...
899 / 28 = 32.107142857143 (the remainder is 3, so 28 is not a divisor of 899)
899 / 29 = 31 (the remainder is 0, so 29 and 31 are divisors of 899)