What are the divisors of 3507?

1, 3, 7, 21, 167, 501, 1169, 3507

There is a total of 8 positive divisors.
The sum of these divisors is 5376.
The arithmetic mean is 672.

8 odd divisors

1, 3, 7, 21, 167, 501, 1169, 3507

How to compute the divisors of 3507?

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 3507 by each of the numbers from 1 to 3507 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)

3507 / 1 = 3507 (the remainder is 0, so 1 is a divisor of 3507)
3507 / 2 = 1753.5 (the remainder is 1, so 2 is not a divisor of 3507)
3507 / 3 = 1169 (the remainder is 0, so 3 is a divisor of 3507)
...
3507 / 3506 = 1.000285225328 (the remainder is 1, so 3506 is not a divisor of 3507)
3507 / 3507 = 1 (the remainder is 0, so 3507 is a divisor of 3507)

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 3507 (i.e. 59.219929077972). 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 $\frac{N}{d} = D$ )

3507 / 1 = 3507 (the remainder is 0, so 1 and 3507 are divisors of 3507)
3507 / 2 = 1753.5 (the remainder is 1, so 2 is not a divisor of 3507)
3507 / 3 = 1169 (the remainder is 0, so 3 and 1169 are divisors of 3507)
...
3507 / 58 = 60.465517241379 (the remainder is 27, so 58 is not a divisor of 3507)
3507 / 59 = 59.440677966102 (the remainder is 26, so 59 is not a divisor of 3507)