What are the divisors of 5062?

1, 2, 2531, 5062

There is a total of 4 positive divisors.
The sum of these divisors is 7596.
The arithmetic mean is 1899.

2 even divisors

2, 5062

2 odd divisors

1, 2531

How to compute the divisors of 5062?

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 5062 by each of the numbers from 1 to 5062 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)

5062 / 1 = 5062 (the remainder is 0, so 1 is a divisor of 5062)
5062 / 2 = 2531 (the remainder is 0, so 2 is a divisor of 5062)
5062 / 3 = 1687.3333333333 (the remainder is 1, so 3 is not a divisor of 5062)
...
5062 / 5061 = 1.0001975894092 (the remainder is 1, so 5061 is not a divisor of 5062)
5062 / 5062 = 1 (the remainder is 0, so 5062 is a divisor of 5062)

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 5062 (i.e. 71.147733625183). 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 $\frac{N}{d} = D$ )

5062 / 1 = 5062 (the remainder is 0, so 1 and 5062 are divisors of 5062)
5062 / 2 = 2531 (the remainder is 0, so 2 and 2531 are divisors of 5062)
5062 / 3 = 1687.3333333333 (the remainder is 1, so 3 is not a divisor of 5062)
...
5062 / 70 = 72.314285714286 (the remainder is 22, so 70 is not a divisor of 5062)
5062 / 71 = 71.295774647887 (the remainder is 21, so 71 is not a divisor of 5062)