What are the divisors of 5153?

1, 5153

There is a total of 2 positive divisors.
The sum of these divisors is 5154.
The arithmetic mean is 2577.

2 odd divisors

1, 5153

How to compute the divisors of 5153?

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 5153 by each of the numbers from 1 to 5153 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)

5153 / 1 = 5153 (the remainder is 0, so 1 is a divisor of 5153)
5153 / 2 = 2576.5 (the remainder is 1, so 2 is not a divisor of 5153)
5153 / 3 = 1717.6666666667 (the remainder is 2, so 3 is not a divisor of 5153)
...
5153 / 5152 = 1.0001940993789 (the remainder is 1, so 5152 is not a divisor of 5153)
5153 / 5153 = 1 (the remainder is 0, so 5153 is a divisor of 5153)

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 5153 (i.e. 71.784399419372). 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 $\frac{N}{d} = D$ )

5153 / 1 = 5153 (the remainder is 0, so 1 and 5153 are divisors of 5153)
5153 / 2 = 2576.5 (the remainder is 1, so 2 is not a divisor of 5153)
5153 / 3 = 1717.6666666667 (the remainder is 2, so 3 is not a divisor of 5153)
...
5153 / 70 = 73.614285714286 (the remainder is 43, so 70 is not a divisor of 5153)
5153 / 71 = 72.577464788732 (the remainder is 41, so 71 is not a divisor of 5153)