What are the divisors of 3732?

1, 2, 3, 4, 6, 12, 311, 622, 933, 1244, 1866, 3732

There is a total of 12 positive divisors.
The sum of these divisors is 8736.
The arithmetic mean is 728.

8 even divisors

2, 4, 6, 12, 622, 1244, 1866, 3732

4 odd divisors

1, 3, 311, 933

How to compute the divisors of 3732?

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 3732 by each of the numbers from 1 to 3732 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)

3732 / 1 = 3732 (the remainder is 0, so 1 is a divisor of 3732)
3732 / 2 = 1866 (the remainder is 0, so 2 is a divisor of 3732)
3732 / 3 = 1244 (the remainder is 0, so 3 is a divisor of 3732)
...
3732 / 3731 = 1.0002680246583 (the remainder is 1, so 3731 is not a divisor of 3732)
3732 / 3732 = 1 (the remainder is 0, so 3732 is a divisor of 3732)

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 3732 (i.e. 61.090097397205). 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 $\frac{N}{d} = D$ )

3732 / 1 = 3732 (the remainder is 0, so 1 and 3732 are divisors of 3732)
3732 / 2 = 1866 (the remainder is 0, so 2 and 1866 are divisors of 3732)
3732 / 3 = 1244 (the remainder is 0, so 3 and 1244 are divisors of 3732)
...
3732 / 60 = 62.2 (the remainder is 12, so 60 is not a divisor of 3732)
3732 / 61 = 61.180327868852 (the remainder is 11, so 61 is not a divisor of 3732)