What are the divisors of 3664?

1, 2, 4, 8, 16, 229, 458, 916, 1832, 3664

There is a total of 10 positive divisors.
The sum of these divisors is 7130.
The arithmetic mean is 713.

8 even divisors

2, 4, 8, 16, 458, 916, 1832, 3664

2 odd divisors

1, 229

How to compute the divisors of 3664?

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 3664 by each of the numbers from 1 to 3664 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)

3664 / 1 = 3664 (the remainder is 0, so 1 is a divisor of 3664)
3664 / 2 = 1832 (the remainder is 0, so 2 is a divisor of 3664)
3664 / 3 = 1221.3333333333 (the remainder is 1, so 3 is not a divisor of 3664)
...
3664 / 3663 = 1.000273000273 (the remainder is 1, so 3663 is not a divisor of 3664)
3664 / 3664 = 1 (the remainder is 0, so 3664 is a divisor of 3664)

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 3664 (i.e. 60.530983801686). 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 $\frac{N}{d} = D$ )

3664 / 1 = 3664 (the remainder is 0, so 1 and 3664 are divisors of 3664)
3664 / 2 = 1832 (the remainder is 0, so 2 and 1832 are divisors of 3664)
3664 / 3 = 1221.3333333333 (the remainder is 1, so 3 is not a divisor of 3664)
...
3664 / 59 = 62.101694915254 (the remainder is 6, so 59 is not a divisor of 3664)
3664 / 60 = 61.066666666667 (the remainder is 4, so 60 is not a divisor of 3664)