What are the divisors of 3755?

1, 5, 751, 3755

There is a total of 4 positive divisors.
The sum of these divisors is 4512.
The arithmetic mean is 1128.

4 odd divisors

1, 5, 751, 3755

How to compute the divisors of 3755?

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 3755 by each of the numbers from 1 to 3755 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)

3755 / 1 = 3755 (the remainder is 0, so 1 is a divisor of 3755)
3755 / 2 = 1877.5 (the remainder is 1, so 2 is not a divisor of 3755)
3755 / 3 = 1251.6666666667 (the remainder is 2, so 3 is not a divisor of 3755)
...
3755 / 3754 = 1.0002663825253 (the remainder is 1, so 3754 is not a divisor of 3755)
3755 / 3755 = 1 (the remainder is 0, so 3755 is a divisor of 3755)

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 3755 (i.e. 61.278054799414). 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 $\frac{N}{d} = D$ )

3755 / 1 = 3755 (the remainder is 0, so 1 and 3755 are divisors of 3755)
3755 / 2 = 1877.5 (the remainder is 1, so 2 is not a divisor of 3755)
3755 / 3 = 1251.6666666667 (the remainder is 2, so 3 is not a divisor of 3755)
...
3755 / 60 = 62.583333333333 (the remainder is 35, so 60 is not a divisor of 3755)
3755 / 61 = 61.55737704918 (the remainder is 34, so 61 is not a divisor of 3755)