What are the divisors of 5221?

1, 23, 227, 5221

There is a total of 4 positive divisors.
The sum of these divisors is 5472.
The arithmetic mean is 1368.

4 odd divisors

1, 23, 227, 5221

How to compute the divisors of 5221?

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 5221 by each of the numbers from 1 to 5221 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)

5221 / 1 = 5221 (the remainder is 0, so 1 is a divisor of 5221)
5221 / 2 = 2610.5 (the remainder is 1, so 2 is not a divisor of 5221)
5221 / 3 = 1740.3333333333 (the remainder is 1, so 3 is not a divisor of 5221)
...
5221 / 5220 = 1.0001915708812 (the remainder is 1, so 5220 is not a divisor of 5221)
5221 / 5221 = 1 (the remainder is 0, so 5221 is a divisor of 5221)

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 5221 (i.e. 72.256487598001). 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 $\frac{N}{d} = D$ )

5221 / 1 = 5221 (the remainder is 0, so 1 and 5221 are divisors of 5221)
5221 / 2 = 2610.5 (the remainder is 1, so 2 is not a divisor of 5221)
5221 / 3 = 1740.3333333333 (the remainder is 1, so 3 is not a divisor of 5221)
...
5221 / 71 = 73.535211267606 (the remainder is 38, so 71 is not a divisor of 5221)
5221 / 72 = 72.513888888889 (the remainder is 37, so 72 is not a divisor of 5221)