What are the divisors of 3517?

1, 3517

There is a total of 2 positive divisors.
The sum of these divisors is 3518.
The arithmetic mean is 1759.

2 odd divisors

1, 3517

How to compute the divisors of 3517?

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 3517 by each of the numbers from 1 to 3517 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)

3517 / 1 = 3517 (the remainder is 0, so 1 is a divisor of 3517)
3517 / 2 = 1758.5 (the remainder is 1, so 2 is not a divisor of 3517)
3517 / 3 = 1172.3333333333 (the remainder is 1, so 3 is not a divisor of 3517)
...
3517 / 3516 = 1.0002844141069 (the remainder is 1, so 3516 is not a divisor of 3517)
3517 / 3517 = 1 (the remainder is 0, so 3517 is a divisor of 3517)

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 3517 (i.e. 59.304300012731). 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 $\frac{N}{d} = D$ )

3517 / 1 = 3517 (the remainder is 0, so 1 and 3517 are divisors of 3517)
3517 / 2 = 1758.5 (the remainder is 1, so 2 is not a divisor of 3517)
3517 / 3 = 1172.3333333333 (the remainder is 1, so 3 is not a divisor of 3517)
...
3517 / 58 = 60.637931034483 (the remainder is 37, so 58 is not a divisor of 3517)
3517 / 59 = 59.610169491525 (the remainder is 36, so 59 is not a divisor of 3517)