What are the divisors of 3529?

1, 3529

There is a total of 2 positive divisors.
The sum of these divisors is 3530.
The arithmetic mean is 1765.

2 odd divisors

1, 3529

How to compute the divisors of 3529?

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 3529 by each of the numbers from 1 to 3529 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)

3529 / 1 = 3529 (the remainder is 0, so 1 is a divisor of 3529)
3529 / 2 = 1764.5 (the remainder is 1, so 2 is not a divisor of 3529)
3529 / 3 = 1176.3333333333 (the remainder is 1, so 3 is not a divisor of 3529)
...
3529 / 3528 = 1.000283446712 (the remainder is 1, so 3528 is not a divisor of 3529)
3529 / 3529 = 1 (the remainder is 0, so 3529 is a divisor of 3529)

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 3529 (i.e. 59.405386961117). 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 $\frac{N}{d} = D$ )

3529 / 1 = 3529 (the remainder is 0, so 1 and 3529 are divisors of 3529)
3529 / 2 = 1764.5 (the remainder is 1, so 2 is not a divisor of 3529)
3529 / 3 = 1176.3333333333 (the remainder is 1, so 3 is not a divisor of 3529)
...
3529 / 58 = 60.844827586207 (the remainder is 49, so 58 is not a divisor of 3529)
3529 / 59 = 59.813559322034 (the remainder is 48, so 59 is not a divisor of 3529)