What are the divisors of 3229?

1, 3229

There is a total of 2 positive divisors.
The sum of these divisors is 3230.
The arithmetic mean is 1615.

2 odd divisors

1, 3229

How to compute the divisors of 3229?

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 3229 by each of the numbers from 1 to 3229 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)

3229 / 1 = 3229 (the remainder is 0, so 1 is a divisor of 3229)
3229 / 2 = 1614.5 (the remainder is 1, so 2 is not a divisor of 3229)
3229 / 3 = 1076.3333333333 (the remainder is 1, so 3 is not a divisor of 3229)
...
3229 / 3228 = 1.0003097893432 (the remainder is 1, so 3228 is not a divisor of 3229)
3229 / 3229 = 1 (the remainder is 0, so 3229 is a divisor of 3229)

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 3229 (i.e. 56.824290580701). 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 $\frac{N}{d} = D$ )

3229 / 1 = 3229 (the remainder is 0, so 1 and 3229 are divisors of 3229)
3229 / 2 = 1614.5 (the remainder is 1, so 2 is not a divisor of 3229)
3229 / 3 = 1076.3333333333 (the remainder is 1, so 3 is not a divisor of 3229)
...
3229 / 55 = 58.709090909091 (the remainder is 39, so 55 is not a divisor of 3229)
3229 / 56 = 57.660714285714 (the remainder is 37, so 56 is not a divisor of 3229)