What are the divisors of 3279?

1, 3, 1093, 3279

There is a total of 4 positive divisors.
The sum of these divisors is 4376.
The arithmetic mean is 1094.

4 odd divisors

1, 3, 1093, 3279

How to compute the divisors of 3279?

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 3279 by each of the numbers from 1 to 3279 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)

3279 / 1 = 3279 (the remainder is 0, so 1 is a divisor of 3279)
3279 / 2 = 1639.5 (the remainder is 1, so 2 is not a divisor of 3279)
3279 / 3 = 1093 (the remainder is 0, so 3 is a divisor of 3279)
...
3279 / 3278 = 1.0003050640635 (the remainder is 1, so 3278 is not a divisor of 3279)
3279 / 3279 = 1 (the remainder is 0, so 3279 is a divisor of 3279)

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 3279 (i.e. 57.262553208882). 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 $\frac{N}{d} = D$ )

3279 / 1 = 3279 (the remainder is 0, so 1 and 3279 are divisors of 3279)
3279 / 2 = 1639.5 (the remainder is 1, so 2 is not a divisor of 3279)
3279 / 3 = 1093 (the remainder is 0, so 3 and 1093 are divisors of 3279)
...
3279 / 56 = 58.553571428571 (the remainder is 31, so 56 is not a divisor of 3279)
3279 / 57 = 57.526315789474 (the remainder is 30, so 57 is not a divisor of 3279)