What are the divisors of 226?

1, 2, 113, 226

There is a total of 4 positive divisors.
The sum of these divisors is 342.
The arithmetic mean is 85.5.

2 even divisors

2, 226

2 odd divisors

1, 113

How to compute the divisors of 226?

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 226 by each of the numbers from 1 to 226 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)

226 / 1 = 226 (the remainder is 0, so 1 is a divisor of 226)
226 / 2 = 113 (the remainder is 0, so 2 is a divisor of 226)
226 / 3 = 75.333333333333 (the remainder is 1, so 3 is not a divisor of 226)
...
226 / 225 = 1.0044444444444 (the remainder is 1, so 225 is not a divisor of 226)
226 / 226 = 1 (the remainder is 0, so 226 is a divisor of 226)

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 226 (i.e. 15.033296378373). 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 $\frac{N}{d} = D$ )

226 / 1 = 226 (the remainder is 0, so 1 and 226 are divisors of 226)
226 / 2 = 113 (the remainder is 0, so 2 and 113 are divisors of 226)
226 / 3 = 75.333333333333 (the remainder is 1, so 3 is not a divisor of 226)
...
226 / 14 = 16.142857142857 (the remainder is 2, so 14 is not a divisor of 226)
226 / 15 = 15.066666666667 (the remainder is 1, so 15 is not a divisor of 226)