What are the divisors of 229?

1, 229

There is a total of 2 positive divisors.
The sum of these divisors is 230.
The arithmetic mean is 115.

2 odd divisors

1, 229

How to compute the divisors of 229?

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 229 by each of the numbers from 1 to 229 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)

229 / 1 = 229 (the remainder is 0, so 1 is a divisor of 229)
229 / 2 = 114.5 (the remainder is 1, so 2 is not a divisor of 229)
229 / 3 = 76.333333333333 (the remainder is 1, so 3 is not a divisor of 229)
...
229 / 228 = 1.0043859649123 (the remainder is 1, so 228 is not a divisor of 229)
229 / 229 = 1 (the remainder is 0, so 229 is a divisor of 229)

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 229 (i.e. 15.132745950422). 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 $\frac{N}{d} = D$ )

229 / 1 = 229 (the remainder is 0, so 1 and 229 are divisors of 229)
229 / 2 = 114.5 (the remainder is 1, so 2 is not a divisor of 229)
229 / 3 = 76.333333333333 (the remainder is 1, so 3 is not a divisor of 229)
...
229 / 14 = 16.357142857143 (the remainder is 5, so 14 is not a divisor of 229)
229 / 15 = 15.266666666667 (the remainder is 4, so 15 is not a divisor of 229)