What are the divisors of 3484?

1, 2, 4, 13, 26, 52, 67, 134, 268, 871, 1742, 3484

There is a total of 12 positive divisors.
The sum of these divisors is 6664.
The arithmetic mean is 555.33333333333.

8 even divisors

2, 4, 26, 52, 134, 268, 1742, 3484

4 odd divisors

1, 13, 67, 871

How to compute the divisors of 3484?

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 3484 by each of the numbers from 1 to 3484 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)

3484 / 1 = 3484 (the remainder is 0, so 1 is a divisor of 3484)
3484 / 2 = 1742 (the remainder is 0, so 2 is a divisor of 3484)
3484 / 3 = 1161.3333333333 (the remainder is 1, so 3 is not a divisor of 3484)
...
3484 / 3483 = 1.0002871088142 (the remainder is 1, so 3483 is not a divisor of 3484)
3484 / 3484 = 1 (the remainder is 0, so 3484 is a divisor of 3484)

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 3484 (i.e. 59.025418253495). 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 $\frac{N}{d} = D$ )

3484 / 1 = 3484 (the remainder is 0, so 1 and 3484 are divisors of 3484)
3484 / 2 = 1742 (the remainder is 0, so 2 and 1742 are divisors of 3484)
3484 / 3 = 1161.3333333333 (the remainder is 1, so 3 is not a divisor of 3484)
...
3484 / 58 = 60.068965517241 (the remainder is 4, so 58 is not a divisor of 3484)
3484 / 59 = 59.050847457627 (the remainder is 3, so 59 is not a divisor of 3484)