What are the divisors of 3499?

1, 3499

There is a total of 2 positive divisors.
The sum of these divisors is 3500.
The arithmetic mean is 1750.

2 odd divisors

1, 3499

How to compute the divisors of 3499?

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 3499 by each of the numbers from 1 to 3499 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)

3499 / 1 = 3499 (the remainder is 0, so 1 is a divisor of 3499)
3499 / 2 = 1749.5 (the remainder is 1, so 2 is not a divisor of 3499)
3499 / 3 = 1166.3333333333 (the remainder is 1, so 3 is not a divisor of 3499)
...
3499 / 3498 = 1.0002858776444 (the remainder is 1, so 3498 is not a divisor of 3499)
3499 / 3499 = 1 (the remainder is 0, so 3499 is a divisor of 3499)

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 3499 (i.e. 59.152345684681). 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 $\frac{N}{d} = D$ )

3499 / 1 = 3499 (the remainder is 0, so 1 and 3499 are divisors of 3499)
3499 / 2 = 1749.5 (the remainder is 1, so 2 is not a divisor of 3499)
3499 / 3 = 1166.3333333333 (the remainder is 1, so 3 is not a divisor of 3499)
...
3499 / 58 = 60.327586206897 (the remainder is 19, so 58 is not a divisor of 3499)
3499 / 59 = 59.305084745763 (the remainder is 18, so 59 is not a divisor of 3499)