What are the divisors of 3759?

1, 3, 7, 21, 179, 537, 1253, 3759

There is a total of 8 positive divisors.
The sum of these divisors is 5760.
The arithmetic mean is 720.

8 odd divisors

1, 3, 7, 21, 179, 537, 1253, 3759

How to compute the divisors of 3759?

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 3759 by each of the numbers from 1 to 3759 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)

3759 / 1 = 3759 (the remainder is 0, so 1 is a divisor of 3759)
3759 / 2 = 1879.5 (the remainder is 1, so 2 is not a divisor of 3759)
3759 / 3 = 1253 (the remainder is 0, so 3 is a divisor of 3759)
...
3759 / 3758 = 1.0002660989888 (the remainder is 1, so 3758 is not a divisor of 3759)
3759 / 3759 = 1 (the remainder is 0, so 3759 is a divisor of 3759)

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 3759 (i.e. 61.310684223877). 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 $\frac{N}{d} = D$ )

3759 / 1 = 3759 (the remainder is 0, so 1 and 3759 are divisors of 3759)
3759 / 2 = 1879.5 (the remainder is 1, so 2 is not a divisor of 3759)
3759 / 3 = 1253 (the remainder is 0, so 3 and 1253 are divisors of 3759)
...
3759 / 60 = 62.65 (the remainder is 39, so 60 is not a divisor of 3759)
3759 / 61 = 61.622950819672 (the remainder is 38, so 61 is not a divisor of 3759)