What are the divisors of 3739?

1, 3739

There is a total of 2 positive divisors.
The sum of these divisors is 3740.
The arithmetic mean is 1870.

2 odd divisors

1, 3739

How to compute the divisors of 3739?

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 3739 by each of the numbers from 1 to 3739 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)

3739 / 1 = 3739 (the remainder is 0, so 1 is a divisor of 3739)
3739 / 2 = 1869.5 (the remainder is 1, so 2 is not a divisor of 3739)
3739 / 3 = 1246.3333333333 (the remainder is 1, so 3 is not a divisor of 3739)
...
3739 / 3738 = 1.0002675227394 (the remainder is 1, so 3738 is not a divisor of 3739)
3739 / 3739 = 1 (the remainder is 0, so 3739 is a divisor of 3739)

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 3739 (i.e. 61.147362984842). 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 $\frac{N}{d} = D$ )

3739 / 1 = 3739 (the remainder is 0, so 1 and 3739 are divisors of 3739)
3739 / 2 = 1869.5 (the remainder is 1, so 2 is not a divisor of 3739)
3739 / 3 = 1246.3333333333 (the remainder is 1, so 3 is not a divisor of 3739)
...
3739 / 60 = 62.316666666667 (the remainder is 19, so 60 is not a divisor of 3739)
3739 / 61 = 61.295081967213 (the remainder is 18, so 61 is not a divisor of 3739)