What are the divisors of 3652?

1, 2, 4, 11, 22, 44, 83, 166, 332, 913, 1826, 3652

There is a total of 12 positive divisors.
The sum of these divisors is 7056.
The arithmetic mean is 588.

8 even divisors

2, 4, 22, 44, 166, 332, 1826, 3652

4 odd divisors

1, 11, 83, 913

How to compute the divisors of 3652?

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 3652 by each of the numbers from 1 to 3652 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)

3652 / 1 = 3652 (the remainder is 0, so 1 is a divisor of 3652)
3652 / 2 = 1826 (the remainder is 0, so 2 is a divisor of 3652)
3652 / 3 = 1217.3333333333 (the remainder is 1, so 3 is not a divisor of 3652)
...
3652 / 3651 = 1.0002738975623 (the remainder is 1, so 3651 is not a divisor of 3652)
3652 / 3652 = 1 (the remainder is 0, so 3652 is a divisor of 3652)

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 3652 (i.e. 60.431779718953). 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 $\frac{N}{d} = D$ )

3652 / 1 = 3652 (the remainder is 0, so 1 and 3652 are divisors of 3652)
3652 / 2 = 1826 (the remainder is 0, so 2 and 1826 are divisors of 3652)
3652 / 3 = 1217.3333333333 (the remainder is 1, so 3 is not a divisor of 3652)
...
3652 / 59 = 61.898305084746 (the remainder is 53, so 59 is not a divisor of 3652)
3652 / 60 = 60.866666666667 (the remainder is 52, so 60 is not a divisor of 3652)