What are the divisors of 3713?

1, 47, 79, 3713

There is a total of 4 positive divisors.
The sum of these divisors is 3840.
The arithmetic mean is 960.

4 odd divisors

1, 47, 79, 3713

How to compute the divisors of 3713?

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 3713 by each of the numbers from 1 to 3713 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)

3713 / 1 = 3713 (the remainder is 0, so 1 is a divisor of 3713)
3713 / 2 = 1856.5 (the remainder is 1, so 2 is not a divisor of 3713)
3713 / 3 = 1237.6666666667 (the remainder is 2, so 3 is not a divisor of 3713)
...
3713 / 3712 = 1.0002693965517 (the remainder is 1, so 3712 is not a divisor of 3713)
3713 / 3713 = 1 (the remainder is 0, so 3713 is a divisor of 3713)

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 3713 (i.e. 60.934390946328). 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 $\frac{N}{d} = D$ )

3713 / 1 = 3713 (the remainder is 0, so 1 and 3713 are divisors of 3713)
3713 / 2 = 1856.5 (the remainder is 1, so 2 is not a divisor of 3713)
3713 / 3 = 1237.6666666667 (the remainder is 2, so 3 is not a divisor of 3713)
...
3713 / 59 = 62.932203389831 (the remainder is 55, so 59 is not a divisor of 3713)
3713 / 60 = 61.883333333333 (the remainder is 53, so 60 is not a divisor of 3713)