What are the divisors of 3423?

1, 3, 7, 21, 163, 489, 1141, 3423

There is a total of 8 positive divisors.
The sum of these divisors is 5248.
The arithmetic mean is 656.

8 odd divisors

1, 3, 7, 21, 163, 489, 1141, 3423

How to compute the divisors of 3423?

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 3423 by each of the numbers from 1 to 3423 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)

3423 / 1 = 3423 (the remainder is 0, so 1 is a divisor of 3423)
3423 / 2 = 1711.5 (the remainder is 1, so 2 is not a divisor of 3423)
3423 / 3 = 1141 (the remainder is 0, so 3 is a divisor of 3423)
...
3423 / 3422 = 1.000292226768 (the remainder is 1, so 3422 is not a divisor of 3423)
3423 / 3423 = 1 (the remainder is 0, so 3423 is a divisor of 3423)

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 3423 (i.e. 58.50640990524). 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 $\frac{N}{d} = D$ )

3423 / 1 = 3423 (the remainder is 0, so 1 and 3423 are divisors of 3423)
3423 / 2 = 1711.5 (the remainder is 1, so 2 is not a divisor of 3423)
3423 / 3 = 1141 (the remainder is 0, so 3 and 1141 are divisors of 3423)
...
3423 / 57 = 60.052631578947 (the remainder is 3, so 57 is not a divisor of 3423)
3423 / 58 = 59.01724137931 (the remainder is 1, so 58 is not a divisor of 3423)