What are the divisors of 3907?

1, 3907

There is a total of 2 positive divisors.
The sum of these divisors is 3908.
The arithmetic mean is 1954.

2 odd divisors

1, 3907

How to compute the divisors of 3907?

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 3907 by each of the numbers from 1 to 3907 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)

3907 / 1 = 3907 (the remainder is 0, so 1 is a divisor of 3907)
3907 / 2 = 1953.5 (the remainder is 1, so 2 is not a divisor of 3907)
3907 / 3 = 1302.3333333333 (the remainder is 1, so 3 is not a divisor of 3907)
...
3907 / 3906 = 1.000256016385 (the remainder is 1, so 3906 is not a divisor of 3907)
3907 / 3907 = 1 (the remainder is 0, so 3907 is a divisor of 3907)

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 3907 (i.e. 62.505999712028). 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 $\frac{N}{d} = D$ )

3907 / 1 = 3907 (the remainder is 0, so 1 and 3907 are divisors of 3907)
3907 / 2 = 1953.5 (the remainder is 1, so 2 is not a divisor of 3907)
3907 / 3 = 1302.3333333333 (the remainder is 1, so 3 is not a divisor of 3907)
...
3907 / 61 = 64.049180327869 (the remainder is 3, so 61 is not a divisor of 3907)
3907 / 62 = 63.016129032258 (the remainder is 1, so 62 is not a divisor of 3907)