What are the divisors of 5063?

1, 61, 83, 5063

There is a total of 4 positive divisors.
The sum of these divisors is 5208.
The arithmetic mean is 1302.

4 odd divisors

1, 61, 83, 5063

How to compute the divisors of 5063?

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 5063 by each of the numbers from 1 to 5063 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)

5063 / 1 = 5063 (the remainder is 0, so 1 is a divisor of 5063)
5063 / 2 = 2531.5 (the remainder is 1, so 2 is not a divisor of 5063)
5063 / 3 = 1687.6666666667 (the remainder is 2, so 3 is not a divisor of 5063)
...
5063 / 5062 = 1.0001975503753 (the remainder is 1, so 5062 is not a divisor of 5063)
5063 / 5063 = 1 (the remainder is 0, so 5063 is a divisor of 5063)

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 5063 (i.e. 71.154760908881). 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 $\frac{N}{d} = D$ )

5063 / 1 = 5063 (the remainder is 0, so 1 and 5063 are divisors of 5063)
5063 / 2 = 2531.5 (the remainder is 1, so 2 is not a divisor of 5063)
5063 / 3 = 1687.6666666667 (the remainder is 2, so 3 is not a divisor of 5063)
...
5063 / 70 = 72.328571428571 (the remainder is 23, so 70 is not a divisor of 5063)
5063 / 71 = 71.30985915493 (the remainder is 22, so 71 is not a divisor of 5063)