What are the divisors of 3919?

1, 3919

There is a total of 2 positive divisors.
The sum of these divisors is 3920.
The arithmetic mean is 1960.

2 odd divisors

1, 3919

How to compute the divisors of 3919?

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 3919 by each of the numbers from 1 to 3919 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)

3919 / 1 = 3919 (the remainder is 0, so 1 is a divisor of 3919)
3919 / 2 = 1959.5 (the remainder is 1, so 2 is not a divisor of 3919)
3919 / 3 = 1306.3333333333 (the remainder is 1, so 3 is not a divisor of 3919)
...
3919 / 3918 = 1.0002552322614 (the remainder is 1, so 3918 is not a divisor of 3919)
3919 / 3919 = 1 (the remainder is 0, so 3919 is a divisor of 3919)

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 3919 (i.e. 62.601916903558). 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 $\frac{N}{d} = D$ )

3919 / 1 = 3919 (the remainder is 0, so 1 and 3919 are divisors of 3919)
3919 / 2 = 1959.5 (the remainder is 1, so 2 is not a divisor of 3919)
3919 / 3 = 1306.3333333333 (the remainder is 1, so 3 is not a divisor of 3919)
...
3919 / 61 = 64.245901639344 (the remainder is 15, so 61 is not a divisor of 3919)
3919 / 62 = 63.209677419355 (the remainder is 13, so 62 is not a divisor of 3919)