What are the divisors of 3523?

1, 13, 271, 3523

There is a total of 4 positive divisors.
The sum of these divisors is 3808.
The arithmetic mean is 952.

4 odd divisors

1, 13, 271, 3523

How to compute the divisors of 3523?

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 3523 by each of the numbers from 1 to 3523 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)

3523 / 1 = 3523 (the remainder is 0, so 1 is a divisor of 3523)
3523 / 2 = 1761.5 (the remainder is 1, so 2 is not a divisor of 3523)
3523 / 3 = 1174.3333333333 (the remainder is 1, so 3 is not a divisor of 3523)
...
3523 / 3522 = 1.0002839295855 (the remainder is 1, so 3522 is not a divisor of 3523)
3523 / 3523 = 1 (the remainder is 0, so 3523 is a divisor of 3523)

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 3523 (i.e. 59.354865007007). 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 $\frac{N}{d} = D$ )

3523 / 1 = 3523 (the remainder is 0, so 1 and 3523 are divisors of 3523)
3523 / 2 = 1761.5 (the remainder is 1, so 2 is not a divisor of 3523)
3523 / 3 = 1174.3333333333 (the remainder is 1, so 3 is not a divisor of 3523)
...
3523 / 58 = 60.741379310345 (the remainder is 43, so 58 is not a divisor of 3523)
3523 / 59 = 59.71186440678 (the remainder is 42, so 59 is not a divisor of 3523)