What are the divisors of 3429?

1, 3, 9, 27, 127, 381, 1143, 3429

There is a total of 8 positive divisors.
The sum of these divisors is 5120.
The arithmetic mean is 640.

8 odd divisors

1, 3, 9, 27, 127, 381, 1143, 3429

How to compute the divisors of 3429?

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 3429 by each of the numbers from 1 to 3429 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)

3429 / 1 = 3429 (the remainder is 0, so 1 is a divisor of 3429)
3429 / 2 = 1714.5 (the remainder is 1, so 2 is not a divisor of 3429)
3429 / 3 = 1143 (the remainder is 0, so 3 is a divisor of 3429)
...
3429 / 3428 = 1.0002917152859 (the remainder is 1, so 3428 is not a divisor of 3429)
3429 / 3429 = 1 (the remainder is 0, so 3429 is a divisor of 3429)

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 3429 (i.e. 58.557663887829). 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 $\frac{N}{d} = D$ )

3429 / 1 = 3429 (the remainder is 0, so 1 and 3429 are divisors of 3429)
3429 / 2 = 1714.5 (the remainder is 1, so 2 is not a divisor of 3429)
3429 / 3 = 1143 (the remainder is 0, so 3 and 1143 are divisors of 3429)
...
3429 / 57 = 60.157894736842 (the remainder is 9, so 57 is not a divisor of 3429)
3429 / 58 = 59.120689655172 (the remainder is 7, so 58 is not a divisor of 3429)