What are the divisors of 3939?

1, 3, 13, 39, 101, 303, 1313, 3939

There is a total of 8 positive divisors.
The sum of these divisors is 5712.
The arithmetic mean is 714.

8 odd divisors

1, 3, 13, 39, 101, 303, 1313, 3939

How to compute the divisors of 3939?

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 3939 by each of the numbers from 1 to 3939 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)

3939 / 1 = 3939 (the remainder is 0, so 1 is a divisor of 3939)
3939 / 2 = 1969.5 (the remainder is 1, so 2 is not a divisor of 3939)
3939 / 3 = 1313 (the remainder is 0, so 3 is a divisor of 3939)
...
3939 / 3938 = 1.0002539360081 (the remainder is 1, so 3938 is not a divisor of 3939)
3939 / 3939 = 1 (the remainder is 0, so 3939 is a divisor of 3939)

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 3939 (i.e. 62.761453138053). 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 $\frac{N}{d} = D$ )

3939 / 1 = 3939 (the remainder is 0, so 1 and 3939 are divisors of 3939)
3939 / 2 = 1969.5 (the remainder is 1, so 2 is not a divisor of 3939)
3939 / 3 = 1313 (the remainder is 0, so 3 and 1313 are divisors of 3939)
...
3939 / 61 = 64.573770491803 (the remainder is 35, so 61 is not a divisor of 3939)
3939 / 62 = 63.532258064516 (the remainder is 33, so 62 is not a divisor of 3939)