What are the divisors of 3644?

1, 2, 4, 911, 1822, 3644

There is a total of 6 positive divisors.
The sum of these divisors is 6384.
The arithmetic mean is 1064.

4 even divisors

2, 4, 1822, 3644

2 odd divisors

1, 911

How to compute the divisors of 3644?

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 3644 by each of the numbers from 1 to 3644 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)

3644 / 1 = 3644 (the remainder is 0, so 1 is a divisor of 3644)
3644 / 2 = 1822 (the remainder is 0, so 2 is a divisor of 3644)
3644 / 3 = 1214.6666666667 (the remainder is 2, so 3 is not a divisor of 3644)
...
3644 / 3643 = 1.0002744990393 (the remainder is 1, so 3643 is not a divisor of 3644)
3644 / 3644 = 1 (the remainder is 0, so 3644 is a divisor of 3644)

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 3644 (i.e. 60.365553091146). 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 $\frac{N}{d} = D$ )

3644 / 1 = 3644 (the remainder is 0, so 1 and 3644 are divisors of 3644)
3644 / 2 = 1822 (the remainder is 0, so 2 and 1822 are divisors of 3644)
3644 / 3 = 1214.6666666667 (the remainder is 2, so 3 is not a divisor of 3644)
...
3644 / 59 = 61.762711864407 (the remainder is 45, so 59 is not a divisor of 3644)
3644 / 60 = 60.733333333333 (the remainder is 44, so 60 is not a divisor of 3644)