What are the divisors of 2229?

1, 3, 743, 2229

There is a total of 4 positive divisors.
The sum of these divisors is 2976.
The arithmetic mean is 744.

4 odd divisors

1, 3, 743, 2229

How to compute the divisors of 2229?

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 2229 by each of the numbers from 1 to 2229 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)

2229 / 1 = 2229 (the remainder is 0, so 1 is a divisor of 2229)
2229 / 2 = 1114.5 (the remainder is 1, so 2 is not a divisor of 2229)
2229 / 3 = 743 (the remainder is 0, so 3 is a divisor of 2229)
...
2229 / 2228 = 1.0004488330341 (the remainder is 1, so 2228 is not a divisor of 2229)
2229 / 2229 = 1 (the remainder is 0, so 2229 is a divisor of 2229)

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 2229 (i.e. 47.212286536452). 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 $\frac{N}{d} = D$ )

2229 / 1 = 2229 (the remainder is 0, so 1 and 2229 are divisors of 2229)
2229 / 2 = 1114.5 (the remainder is 1, so 2 is not a divisor of 2229)
2229 / 3 = 743 (the remainder is 0, so 3 and 743 are divisors of 2229)
...
2229 / 46 = 48.45652173913 (the remainder is 21, so 46 is not a divisor of 2229)
2229 / 47 = 47.425531914894 (the remainder is 20, so 47 is not a divisor of 2229)