What are the divisors of 5027?

1, 11, 457, 5027

There is a total of 4 positive divisors.
The sum of these divisors is 5496.
The arithmetic mean is 1374.

4 odd divisors

1, 11, 457, 5027

How to compute the divisors of 5027?

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 5027 by each of the numbers from 1 to 5027 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)

5027 / 1 = 5027 (the remainder is 0, so 1 is a divisor of 5027)
5027 / 2 = 2513.5 (the remainder is 1, so 2 is not a divisor of 5027)
5027 / 3 = 1675.6666666667 (the remainder is 2, so 3 is not a divisor of 5027)
...
5027 / 5026 = 1.00019896538 (the remainder is 1, so 5026 is not a divisor of 5027)
5027 / 5027 = 1 (the remainder is 0, so 5027 is a divisor of 5027)

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 5027 (i.e. 70.901339902713). 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 $\frac{N}{d} = D$ )

5027 / 1 = 5027 (the remainder is 0, so 1 and 5027 are divisors of 5027)
5027 / 2 = 2513.5 (the remainder is 1, so 2 is not a divisor of 5027)
5027 / 3 = 1675.6666666667 (the remainder is 2, so 3 is not a divisor of 5027)
...
5027 / 69 = 72.855072463768 (the remainder is 59, so 69 is not a divisor of 5027)
5027 / 70 = 71.814285714286 (the remainder is 57, so 70 is not a divisor of 5027)