What are the divisors of 3524?

1, 2, 4, 881, 1762, 3524

There is a total of 6 positive divisors.
The sum of these divisors is 6174.
The arithmetic mean is 1029.

4 even divisors

2, 4, 1762, 3524

2 odd divisors

1, 881

How to compute the divisors of 3524?

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 3524 by each of the numbers from 1 to 3524 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)

3524 / 1 = 3524 (the remainder is 0, so 1 is a divisor of 3524)
3524 / 2 = 1762 (the remainder is 0, so 2 is a divisor of 3524)
3524 / 3 = 1174.6666666667 (the remainder is 2, so 3 is not a divisor of 3524)
...
3524 / 3523 = 1.0002838489923 (the remainder is 1, so 3523 is not a divisor of 3524)
3524 / 3524 = 1 (the remainder is 0, so 3524 is a divisor of 3524)

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 3524 (i.e. 59.363288318623). 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 $\frac{N}{d} = D$ )

3524 / 1 = 3524 (the remainder is 0, so 1 and 3524 are divisors of 3524)
3524 / 2 = 1762 (the remainder is 0, so 2 and 1762 are divisors of 3524)
3524 / 3 = 1174.6666666667 (the remainder is 2, so 3 is not a divisor of 3524)
...
3524 / 58 = 60.758620689655 (the remainder is 44, so 58 is not a divisor of 3524)
3524 / 59 = 59.728813559322 (the remainder is 43, so 59 is not a divisor of 3524)