What are the divisors of 3446?

1, 2, 1723, 3446

There is a total of 4 positive divisors.
The sum of these divisors is 5172.
The arithmetic mean is 1293.

2 even divisors

2, 3446

2 odd divisors

1, 1723

How to compute the divisors of 3446?

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 3446 by each of the numbers from 1 to 3446 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)

3446 / 1 = 3446 (the remainder is 0, so 1 is a divisor of 3446)
3446 / 2 = 1723 (the remainder is 0, so 2 is a divisor of 3446)
3446 / 3 = 1148.6666666667 (the remainder is 2, so 3 is not a divisor of 3446)
...
3446 / 3445 = 1.000290275762 (the remainder is 1, so 3445 is not a divisor of 3446)
3446 / 3446 = 1 (the remainder is 0, so 3446 is a divisor of 3446)

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 3446 (i.e. 58.702640485757). 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 $\frac{N}{d} = D$ )

3446 / 1 = 3446 (the remainder is 0, so 1 and 3446 are divisors of 3446)
3446 / 2 = 1723 (the remainder is 0, so 2 and 1723 are divisors of 3446)
3446 / 3 = 1148.6666666667 (the remainder is 2, so 3 is not a divisor of 3446)
...
3446 / 57 = 60.456140350877 (the remainder is 26, so 57 is not a divisor of 3446)
3446 / 58 = 59.413793103448 (the remainder is 24, so 58 is not a divisor of 3446)