What are the divisors of 5242?

1, 2, 2621, 5242

There is a total of 4 positive divisors.
The sum of these divisors is 7866.
The arithmetic mean is 1966.5.

2 even divisors

2, 5242

2 odd divisors

1, 2621

How to compute the divisors of 5242?

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 5242 by each of the numbers from 1 to 5242 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)

5242 / 1 = 5242 (the remainder is 0, so 1 is a divisor of 5242)
5242 / 2 = 2621 (the remainder is 0, so 2 is a divisor of 5242)
5242 / 3 = 1747.3333333333 (the remainder is 1, so 3 is not a divisor of 5242)
...
5242 / 5241 = 1.0001908032818 (the remainder is 1, so 5241 is not a divisor of 5242)
5242 / 5242 = 1 (the remainder is 0, so 5242 is a divisor of 5242)

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 5242 (i.e. 72.401657439592). 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 $\frac{N}{d} = D$ )

5242 / 1 = 5242 (the remainder is 0, so 1 and 5242 are divisors of 5242)
5242 / 2 = 2621 (the remainder is 0, so 2 and 2621 are divisors of 5242)
5242 / 3 = 1747.3333333333 (the remainder is 1, so 3 is not a divisor of 5242)
...
5242 / 71 = 73.830985915493 (the remainder is 59, so 71 is not a divisor of 5242)
5242 / 72 = 72.805555555556 (the remainder is 58, so 72 is not a divisor of 5242)