What are the divisors of 3536?

1, 2, 4, 8, 13, 16, 17, 26, 34, 52, 68, 104, 136, 208, 221, 272, 442, 884, 1768, 3536

There is a total of 20 positive divisors.
The sum of these divisors is 7812.
The arithmetic mean is 390.6.

16 even divisors

2, 4, 8, 16, 26, 34, 52, 68, 104, 136, 208, 272, 442, 884, 1768, 3536

4 odd divisors

1, 13, 17, 221

How to compute the divisors of 3536?

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 3536 by each of the numbers from 1 to 3536 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)

3536 / 1 = 3536 (the remainder is 0, so 1 is a divisor of 3536)
3536 / 2 = 1768 (the remainder is 0, so 2 is a divisor of 3536)
3536 / 3 = 1178.6666666667 (the remainder is 2, so 3 is not a divisor of 3536)
...
3536 / 3535 = 1.0002828854314 (the remainder is 1, so 3535 is not a divisor of 3536)
3536 / 3536 = 1 (the remainder is 0, so 3536 is a divisor of 3536)

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 3536 (i.e. 59.464274989274). 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 $\frac{N}{d} = D$ )

3536 / 1 = 3536 (the remainder is 0, so 1 and 3536 are divisors of 3536)
3536 / 2 = 1768 (the remainder is 0, so 2 and 1768 are divisors of 3536)
3536 / 3 = 1178.6666666667 (the remainder is 2, so 3 is not a divisor of 3536)
...
3536 / 58 = 60.965517241379 (the remainder is 56, so 58 is not a divisor of 3536)
3536 / 59 = 59.932203389831 (the remainder is 55, so 59 is not a divisor of 3536)