What are the divisors of 3632?

1, 2, 4, 8, 16, 227, 454, 908, 1816, 3632

There is a total of 10 positive divisors.
The sum of these divisors is 7068.
The arithmetic mean is 706.8.

8 even divisors

2, 4, 8, 16, 454, 908, 1816, 3632

2 odd divisors

1, 227

How to compute the divisors of 3632?

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 3632 by each of the numbers from 1 to 3632 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)

3632 / 1 = 3632 (the remainder is 0, so 1 is a divisor of 3632)
3632 / 2 = 1816 (the remainder is 0, so 2 is a divisor of 3632)
3632 / 3 = 1210.6666666667 (the remainder is 2, so 3 is not a divisor of 3632)
...
3632 / 3631 = 1.0002754062242 (the remainder is 1, so 3631 is not a divisor of 3632)
3632 / 3632 = 1 (the remainder is 0, so 3632 is a divisor of 3632)

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 3632 (i.e. 60.266076693277). 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 $\frac{N}{d} = D$ )

3632 / 1 = 3632 (the remainder is 0, so 1 and 3632 are divisors of 3632)
3632 / 2 = 1816 (the remainder is 0, so 2 and 1816 are divisors of 3632)
3632 / 3 = 1210.6666666667 (the remainder is 2, so 3 is not a divisor of 3632)
...
3632 / 59 = 61.559322033898 (the remainder is 33, so 59 is not a divisor of 3632)
3632 / 60 = 60.533333333333 (the remainder is 32, so 60 is not a divisor of 3632)