What are the divisors of 3707?

1, 11, 337, 3707

There is a total of 4 positive divisors.
The sum of these divisors is 4056.
The arithmetic mean is 1014.

4 odd divisors

1, 11, 337, 3707

How to compute the divisors of 3707?

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 3707 by each of the numbers from 1 to 3707 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)

3707 / 1 = 3707 (the remainder is 0, so 1 is a divisor of 3707)
3707 / 2 = 1853.5 (the remainder is 1, so 2 is not a divisor of 3707)
3707 / 3 = 1235.6666666667 (the remainder is 2, so 3 is not a divisor of 3707)
...
3707 / 3706 = 1.0002698327037 (the remainder is 1, so 3706 is not a divisor of 3707)
3707 / 3707 = 1 (the remainder is 0, so 3707 is a divisor of 3707)

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 3707 (i.e. 60.885137759555). 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 $\frac{N}{d} = D$ )

3707 / 1 = 3707 (the remainder is 0, so 1 and 3707 are divisors of 3707)
3707 / 2 = 1853.5 (the remainder is 1, so 2 is not a divisor of 3707)
3707 / 3 = 1235.6666666667 (the remainder is 2, so 3 is not a divisor of 3707)
...
3707 / 59 = 62.830508474576 (the remainder is 49, so 59 is not a divisor of 3707)
3707 / 60 = 61.783333333333 (the remainder is 47, so 60 is not a divisor of 3707)