What are the divisors of 5007?

1, 3, 1669, 5007

There is a total of 4 positive divisors.
The sum of these divisors is 6680.
The arithmetic mean is 1670.

4 odd divisors

1, 3, 1669, 5007

How to compute the divisors of 5007?

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 5007 by each of the numbers from 1 to 5007 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)

5007 / 1 = 5007 (the remainder is 0, so 1 is a divisor of 5007)
5007 / 2 = 2503.5 (the remainder is 1, so 2 is not a divisor of 5007)
5007 / 3 = 1669 (the remainder is 0, so 3 is a divisor of 5007)
...
5007 / 5006 = 1.0001997602877 (the remainder is 1, so 5006 is not a divisor of 5007)
5007 / 5007 = 1 (the remainder is 0, so 5007 is a divisor of 5007)

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 5007 (i.e. 70.760158281338). 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 $\frac{N}{d} = D$ )

5007 / 1 = 5007 (the remainder is 0, so 1 and 5007 are divisors of 5007)
5007 / 2 = 2503.5 (the remainder is 1, so 2 is not a divisor of 5007)
5007 / 3 = 1669 (the remainder is 0, so 3 and 1669 are divisors of 5007)
...
5007 / 69 = 72.565217391304 (the remainder is 39, so 69 is not a divisor of 5007)
5007 / 70 = 71.528571428571 (the remainder is 37, so 70 is not a divisor of 5007)