What are the divisors of 3449?

1, 3449

There is a total of 2 positive divisors.
The sum of these divisors is 3450.
The arithmetic mean is 1725.

2 odd divisors

1, 3449

How to compute the divisors of 3449?

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 3449 by each of the numbers from 1 to 3449 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)

3449 / 1 = 3449 (the remainder is 0, so 1 is a divisor of 3449)
3449 / 2 = 1724.5 (the remainder is 1, so 2 is not a divisor of 3449)
3449 / 3 = 1149.6666666667 (the remainder is 2, so 3 is not a divisor of 3449)
...
3449 / 3448 = 1.0002900232019 (the remainder is 1, so 3448 is not a divisor of 3449)
3449 / 3449 = 1 (the remainder is 0, so 3449 is a divisor of 3449)

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 3449 (i.e. 58.728187440104). 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 $\frac{N}{d} = D$ )

3449 / 1 = 3449 (the remainder is 0, so 1 and 3449 are divisors of 3449)
3449 / 2 = 1724.5 (the remainder is 1, so 2 is not a divisor of 3449)
3449 / 3 = 1149.6666666667 (the remainder is 2, so 3 is not a divisor of 3449)
...
3449 / 57 = 60.508771929825 (the remainder is 29, so 57 is not a divisor of 3449)
3449 / 58 = 59.465517241379 (the remainder is 27, so 58 is not a divisor of 3449)