What are the divisors of 5001?

1, 3, 1667, 5001

There is a total of 4 positive divisors.
The sum of these divisors is 6672.
The arithmetic mean is 1668.

4 odd divisors

1, 3, 1667, 5001

How to compute the divisors of 5001?

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 5001 by each of the numbers from 1 to 5001 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)

5001 / 1 = 5001 (the remainder is 0, so 1 is a divisor of 5001)
5001 / 2 = 2500.5 (the remainder is 1, so 2 is not a divisor of 5001)
5001 / 3 = 1667 (the remainder is 0, so 3 is a divisor of 5001)
...
5001 / 5000 = 1.0002 (the remainder is 1, so 5000 is not a divisor of 5001)
5001 / 5001 = 1 (the remainder is 0, so 5001 is a divisor of 5001)

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 5001 (i.e. 70.717748832949). 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 $\frac{N}{d} = D$ )

5001 / 1 = 5001 (the remainder is 0, so 1 and 5001 are divisors of 5001)
5001 / 2 = 2500.5 (the remainder is 1, so 2 is not a divisor of 5001)
5001 / 3 = 1667 (the remainder is 0, so 3 and 1667 are divisors of 5001)
...
5001 / 69 = 72.478260869565 (the remainder is 33, so 69 is not a divisor of 5001)
5001 / 70 = 71.442857142857 (the remainder is 31, so 70 is not a divisor of 5001)