What are the divisors of 3493?

1, 7, 499, 3493

There is a total of 4 positive divisors.
The sum of these divisors is 4000.
The arithmetic mean is 1000.

4 odd divisors

1, 7, 499, 3493

How to compute the divisors of 3493?

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 3493 by each of the numbers from 1 to 3493 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)

3493 / 1 = 3493 (the remainder is 0, so 1 is a divisor of 3493)
3493 / 2 = 1746.5 (the remainder is 1, so 2 is not a divisor of 3493)
3493 / 3 = 1164.3333333333 (the remainder is 1, so 3 is not a divisor of 3493)
...
3493 / 3492 = 1.0002863688431 (the remainder is 1, so 3492 is not a divisor of 3493)
3493 / 3493 = 1 (the remainder is 0, so 3493 is a divisor of 3493)

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 3493 (i.e. 59.101607423149). 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 $\frac{N}{d} = D$ )

3493 / 1 = 3493 (the remainder is 0, so 1 and 3493 are divisors of 3493)
3493 / 2 = 1746.5 (the remainder is 1, so 2 is not a divisor of 3493)
3493 / 3 = 1164.3333333333 (the remainder is 1, so 3 is not a divisor of 3493)
...
3493 / 58 = 60.224137931034 (the remainder is 13, so 58 is not a divisor of 3493)
3493 / 59 = 59.203389830508 (the remainder is 12, so 59 is not a divisor of 3493)