What are the divisors of 5042?

1, 2, 2521, 5042

There is a total of 4 positive divisors.
The sum of these divisors is 7566.
The arithmetic mean is 1891.5.

2 even divisors

2, 5042

2 odd divisors

1, 2521

How to compute the divisors of 5042?

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 5042 by each of the numbers from 1 to 5042 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)

5042 / 1 = 5042 (the remainder is 0, so 1 is a divisor of 5042)
5042 / 2 = 2521 (the remainder is 0, so 2 is a divisor of 5042)
5042 / 3 = 1680.6666666667 (the remainder is 2, so 3 is not a divisor of 5042)
...
5042 / 5041 = 1.0001983733386 (the remainder is 1, so 5041 is not a divisor of 5042)
5042 / 5042 = 1 (the remainder is 0, so 5042 is a divisor of 5042)

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 5042 (i.e. 71.007041904307). 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 $\frac{N}{d} = D$ )

5042 / 1 = 5042 (the remainder is 0, so 1 and 5042 are divisors of 5042)
5042 / 2 = 2521 (the remainder is 0, so 2 and 2521 are divisors of 5042)
5042 / 3 = 1680.6666666667 (the remainder is 2, so 3 is not a divisor of 5042)
...
5042 / 70 = 72.028571428571 (the remainder is 2, so 70 is not a divisor of 5042)
5042 / 71 = 71.014084507042 (the remainder is 1, so 71 is not a divisor of 5042)