What are the divisors of 3764?

1, 2, 4, 941, 1882, 3764

There is a total of 6 positive divisors.
The sum of these divisors is 6594.
The arithmetic mean is 1099.

4 even divisors

2, 4, 1882, 3764

2 odd divisors

1, 941

How to compute the divisors of 3764?

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 3764 by each of the numbers from 1 to 3764 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)

3764 / 1 = 3764 (the remainder is 0, so 1 is a divisor of 3764)
3764 / 2 = 1882 (the remainder is 0, so 2 is a divisor of 3764)
3764 / 3 = 1254.6666666667 (the remainder is 2, so 3 is not a divisor of 3764)
...
3764 / 3763 = 1.0002657454159 (the remainder is 1, so 3763 is not a divisor of 3764)
3764 / 3764 = 1 (the remainder is 0, so 3764 is a divisor of 3764)

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 3764 (i.e. 61.351446600712). 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 $\frac{N}{d} = D$ )

3764 / 1 = 3764 (the remainder is 0, so 1 and 3764 are divisors of 3764)
3764 / 2 = 1882 (the remainder is 0, so 2 and 1882 are divisors of 3764)
3764 / 3 = 1254.6666666667 (the remainder is 2, so 3 is not a divisor of 3764)
...
3764 / 60 = 62.733333333333 (the remainder is 44, so 60 is not a divisor of 3764)
3764 / 61 = 61.704918032787 (the remainder is 43, so 61 is not a divisor of 3764)