What are the divisors of 3709?

1, 3709

There is a total of 2 positive divisors.
The sum of these divisors is 3710.
The arithmetic mean is 1855.

2 odd divisors

1, 3709

How to compute the divisors of 3709?

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 3709 by each of the numbers from 1 to 3709 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)

3709 / 1 = 3709 (the remainder is 0, so 1 is a divisor of 3709)
3709 / 2 = 1854.5 (the remainder is 1, so 2 is not a divisor of 3709)
3709 / 3 = 1236.3333333333 (the remainder is 1, so 3 is not a divisor of 3709)
...
3709 / 3708 = 1.0002696871629 (the remainder is 1, so 3708 is not a divisor of 3709)
3709 / 3709 = 1 (the remainder is 0, so 3709 is a divisor of 3709)

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 3709 (i.e. 60.90155991434). 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 $\frac{N}{d} = D$ )

3709 / 1 = 3709 (the remainder is 0, so 1 and 3709 are divisors of 3709)
3709 / 2 = 1854.5 (the remainder is 1, so 2 is not a divisor of 3709)
3709 / 3 = 1236.3333333333 (the remainder is 1, so 3 is not a divisor of 3709)
...
3709 / 59 = 62.864406779661 (the remainder is 51, so 59 is not a divisor of 3709)
3709 / 60 = 61.816666666667 (the remainder is 49, so 60 is not a divisor of 3709)