What are the divisors of 3508?

1, 2, 4, 877, 1754, 3508

There is a total of 6 positive divisors.
The sum of these divisors is 6146.
The arithmetic mean is 1024.3333333333.

4 even divisors

2, 4, 1754, 3508

2 odd divisors

1, 877

How to compute the divisors of 3508?

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 3508 by each of the numbers from 1 to 3508 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)

3508 / 1 = 3508 (the remainder is 0, so 1 is a divisor of 3508)
3508 / 2 = 1754 (the remainder is 0, so 2 is a divisor of 3508)
3508 / 3 = 1169.3333333333 (the remainder is 1, so 3 is not a divisor of 3508)
...
3508 / 3507 = 1.0002851439977 (the remainder is 1, so 3507 is not a divisor of 3508)
3508 / 3508 = 1 (the remainder is 0, so 3508 is a divisor of 3508)

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 3508 (i.e. 59.228371579843). 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 $\frac{N}{d} = D$ )

3508 / 1 = 3508 (the remainder is 0, so 1 and 3508 are divisors of 3508)
3508 / 2 = 1754 (the remainder is 0, so 2 and 1754 are divisors of 3508)
3508 / 3 = 1169.3333333333 (the remainder is 1, so 3 is not a divisor of 3508)
...
3508 / 58 = 60.48275862069 (the remainder is 28, so 58 is not a divisor of 3508)
3508 / 59 = 59.457627118644 (the remainder is 27, so 59 is not a divisor of 3508)