What are the divisors of 3515?

1, 5, 19, 37, 95, 185, 703, 3515

There is a total of 8 positive divisors.
The sum of these divisors is 4560.
The arithmetic mean is 570.

8 odd divisors

1, 5, 19, 37, 95, 185, 703, 3515

How to compute the divisors of 3515?

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 3515 by each of the numbers from 1 to 3515 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)

3515 / 1 = 3515 (the remainder is 0, so 1 is a divisor of 3515)
3515 / 2 = 1757.5 (the remainder is 1, so 2 is not a divisor of 3515)
3515 / 3 = 1171.6666666667 (the remainder is 2, so 3 is not a divisor of 3515)
...
3515 / 3514 = 1.0002845759818 (the remainder is 1, so 3514 is not a divisor of 3515)
3515 / 3515 = 1 (the remainder is 0, so 3515 is a divisor of 3515)

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 3515 (i.e. 59.287435431127). 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 $\frac{N}{d} = D$ )

3515 / 1 = 3515 (the remainder is 0, so 1 and 3515 are divisors of 3515)
3515 / 2 = 1757.5 (the remainder is 1, so 2 is not a divisor of 3515)
3515 / 3 = 1171.6666666667 (the remainder is 2, so 3 is not a divisor of 3515)
...
3515 / 58 = 60.603448275862 (the remainder is 35, so 58 is not a divisor of 3515)
3515 / 59 = 59.576271186441 (the remainder is 34, so 59 is not a divisor of 3515)