What are the divisors of 3464?

1, 2, 4, 8, 433, 866, 1732, 3464

There is a total of 8 positive divisors.
The sum of these divisors is 6510.
The arithmetic mean is 813.75.

6 even divisors

2, 4, 8, 866, 1732, 3464

2 odd divisors

1, 433

How to compute the divisors of 3464?

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 3464 by each of the numbers from 1 to 3464 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)

3464 / 1 = 3464 (the remainder is 0, so 1 is a divisor of 3464)
3464 / 2 = 1732 (the remainder is 0, so 2 is a divisor of 3464)
3464 / 3 = 1154.6666666667 (the remainder is 2, so 3 is not a divisor of 3464)
...
3464 / 3463 = 1.0002887669651 (the remainder is 1, so 3463 is not a divisor of 3464)
3464 / 3464 = 1 (the remainder is 0, so 3464 is a divisor of 3464)

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 3464 (i.e. 58.855755878249). 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 $\frac{N}{d} = D$ )

3464 / 1 = 3464 (the remainder is 0, so 1 and 3464 are divisors of 3464)
3464 / 2 = 1732 (the remainder is 0, so 2 and 1732 are divisors of 3464)
3464 / 3 = 1154.6666666667 (the remainder is 2, so 3 is not a divisor of 3464)
...
3464 / 57 = 60.771929824561 (the remainder is 44, so 57 is not a divisor of 3464)
3464 / 58 = 59.724137931034 (the remainder is 42, so 58 is not a divisor of 3464)