What are the divisors of 5282?

1, 2, 19, 38, 139, 278, 2641, 5282

There is a total of 8 positive divisors.
The sum of these divisors is 8400.
The arithmetic mean is 1050.

4 even divisors

2, 38, 278, 5282

4 odd divisors

1, 19, 139, 2641

How to compute the divisors of 5282?

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 5282 by each of the numbers from 1 to 5282 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)

5282 / 1 = 5282 (the remainder is 0, so 1 is a divisor of 5282)
5282 / 2 = 2641 (the remainder is 0, so 2 is a divisor of 5282)
5282 / 3 = 1760.6666666667 (the remainder is 2, so 3 is not a divisor of 5282)
...
5282 / 5281 = 1.0001893580761 (the remainder is 1, so 5281 is not a divisor of 5282)
5282 / 5282 = 1 (the remainder is 0, so 5282 is a divisor of 5282)

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 5282 (i.e. 72.677369242426). 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 $\frac{N}{d} = D$ )

5282 / 1 = 5282 (the remainder is 0, so 1 and 5282 are divisors of 5282)
5282 / 2 = 2641 (the remainder is 0, so 2 and 2641 are divisors of 5282)
5282 / 3 = 1760.6666666667 (the remainder is 2, so 3 is not a divisor of 5282)
...
5282 / 71 = 74.394366197183 (the remainder is 28, so 71 is not a divisor of 5282)
5282 / 72 = 73.361111111111 (the remainder is 26, so 72 is not a divisor of 5282)