What are the divisors of 3751?

1, 11, 31, 121, 341, 3751

There is a total of 6 positive divisors.
The sum of these divisors is 4256.
The arithmetic mean is 709.33333333333.

6 odd divisors

1, 11, 31, 121, 341, 3751

How to compute the divisors of 3751?

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 3751 by each of the numbers from 1 to 3751 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)

3751 / 1 = 3751 (the remainder is 0, so 1 is a divisor of 3751)
3751 / 2 = 1875.5 (the remainder is 1, so 2 is not a divisor of 3751)
3751 / 3 = 1250.3333333333 (the remainder is 1, so 3 is not a divisor of 3751)
...
3751 / 3750 = 1.0002666666667 (the remainder is 1, so 3750 is not a divisor of 3751)
3751 / 3751 = 1 (the remainder is 0, so 3751 is a divisor of 3751)

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 3751 (i.e. 61.24540799113). 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 $\frac{N}{d} = D$ )

3751 / 1 = 3751 (the remainder is 0, so 1 and 3751 are divisors of 3751)
3751 / 2 = 1875.5 (the remainder is 1, so 2 is not a divisor of 3751)
3751 / 3 = 1250.3333333333 (the remainder is 1, so 3 is not a divisor of 3751)
...
3751 / 60 = 62.516666666667 (the remainder is 31, so 60 is not a divisor of 3751)
3751 / 61 = 61.491803278689 (the remainder is 30, so 61 is not a divisor of 3751)