What are the divisors of 3765?

1, 3, 5, 15, 251, 753, 1255, 3765

There is a total of 8 positive divisors.
The sum of these divisors is 6048.
The arithmetic mean is 756.

8 odd divisors

1, 3, 5, 15, 251, 753, 1255, 3765

How to compute the divisors of 3765?

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 3765 by each of the numbers from 1 to 3765 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)

3765 / 1 = 3765 (the remainder is 0, so 1 is a divisor of 3765)
3765 / 2 = 1882.5 (the remainder is 1, so 2 is not a divisor of 3765)
3765 / 3 = 1255 (the remainder is 0, so 3 is a divisor of 3765)
...
3765 / 3764 = 1.000265674814 (the remainder is 1, so 3764 is not a divisor of 3765)
3765 / 3765 = 1 (the remainder is 0, so 3765 is a divisor of 3765)

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 3765 (i.e. 61.35959582657). 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 $\frac{N}{d} = D$ )

3765 / 1 = 3765 (the remainder is 0, so 1 and 3765 are divisors of 3765)
3765 / 2 = 1882.5 (the remainder is 1, so 2 is not a divisor of 3765)
3765 / 3 = 1255 (the remainder is 0, so 3 and 1255 are divisors of 3765)
...
3765 / 60 = 62.75 (the remainder is 45, so 60 is not a divisor of 3765)
3765 / 61 = 61.72131147541 (the remainder is 44, so 61 is not a divisor of 3765)