What are the divisors of 3532?

1, 2, 4, 883, 1766, 3532

There is a total of 6 positive divisors.
The sum of these divisors is 6188.
The arithmetic mean is 1031.3333333333.

4 even divisors

2, 4, 1766, 3532

2 odd divisors

1, 883

How to compute the divisors of 3532?

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 3532 by each of the numbers from 1 to 3532 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)

3532 / 1 = 3532 (the remainder is 0, so 1 is a divisor of 3532)
3532 / 2 = 1766 (the remainder is 0, so 2 is a divisor of 3532)
3532 / 3 = 1177.3333333333 (the remainder is 1, so 3 is not a divisor of 3532)
...
3532 / 3531 = 1.0002832058907 (the remainder is 1, so 3531 is not a divisor of 3532)
3532 / 3532 = 1 (the remainder is 0, so 3532 is a divisor of 3532)

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 3532 (i.e. 59.430631832415). 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 $\frac{N}{d} = D$ )

3532 / 1 = 3532 (the remainder is 0, so 1 and 3532 are divisors of 3532)
3532 / 2 = 1766 (the remainder is 0, so 2 and 1766 are divisors of 3532)
3532 / 3 = 1177.3333333333 (the remainder is 1, so 3 is not a divisor of 3532)
...
3532 / 58 = 60.896551724138 (the remainder is 52, so 58 is not a divisor of 3532)
3532 / 59 = 59.864406779661 (the remainder is 51, so 59 is not a divisor of 3532)