What are the divisors of 5053?

1, 31, 163, 5053

There is a total of 4 positive divisors.
The sum of these divisors is 5248.
The arithmetic mean is 1312.

4 odd divisors

1, 31, 163, 5053

How to compute the divisors of 5053?

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 5053 by each of the numbers from 1 to 5053 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)

5053 / 1 = 5053 (the remainder is 0, so 1 is a divisor of 5053)
5053 / 2 = 2526.5 (the remainder is 1, so 2 is not a divisor of 5053)
5053 / 3 = 1684.3333333333 (the remainder is 1, so 3 is not a divisor of 5053)
...
5053 / 5052 = 1.0001979414093 (the remainder is 1, so 5052 is not a divisor of 5053)
5053 / 5053 = 1 (the remainder is 0, so 5053 is a divisor of 5053)

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 5053 (i.e. 71.084456810192). 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 $\frac{N}{d} = D$ )

5053 / 1 = 5053 (the remainder is 0, so 1 and 5053 are divisors of 5053)
5053 / 2 = 2526.5 (the remainder is 1, so 2 is not a divisor of 5053)
5053 / 3 = 1684.3333333333 (the remainder is 1, so 3 is not a divisor of 5053)
...
5053 / 70 = 72.185714285714 (the remainder is 13, so 70 is not a divisor of 5053)
5053 / 71 = 71.169014084507 (the remainder is 12, so 71 is not a divisor of 5053)