What are the divisors of 3736?

1, 2, 4, 8, 467, 934, 1868, 3736

There is a total of 8 positive divisors.
The sum of these divisors is 7020.
The arithmetic mean is 877.5.

6 even divisors

2, 4, 8, 934, 1868, 3736

2 odd divisors

1, 467

How to compute the divisors of 3736?

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 3736 by each of the numbers from 1 to 3736 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)

3736 / 1 = 3736 (the remainder is 0, so 1 is a divisor of 3736)
3736 / 2 = 1868 (the remainder is 0, so 2 is a divisor of 3736)
3736 / 3 = 1245.3333333333 (the remainder is 1, so 3 is not a divisor of 3736)
...
3736 / 3735 = 1.0002677376171 (the remainder is 1, so 3735 is not a divisor of 3736)
3736 / 3736 = 1 (the remainder is 0, so 3736 is a divisor of 3736)

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 3736 (i.e. 61.122827159745). 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 $\frac{N}{d} = D$ )

3736 / 1 = 3736 (the remainder is 0, so 1 and 3736 are divisors of 3736)
3736 / 2 = 1868 (the remainder is 0, so 2 and 1868 are divisors of 3736)
3736 / 3 = 1245.3333333333 (the remainder is 1, so 3 is not a divisor of 3736)
...
3736 / 60 = 62.266666666667 (the remainder is 16, so 60 is not a divisor of 3736)
3736 / 61 = 61.245901639344 (the remainder is 15, so 61 is not a divisor of 3736)