What are the divisors of 5273?

1, 5273

There is a total of 2 positive divisors.
The sum of these divisors is 5274.
The arithmetic mean is 2637.

2 odd divisors

1, 5273

How to compute the divisors of 5273?

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 5273 by each of the numbers from 1 to 5273 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)

5273 / 1 = 5273 (the remainder is 0, so 1 is a divisor of 5273)
5273 / 2 = 2636.5 (the remainder is 1, so 2 is not a divisor of 5273)
5273 / 3 = 1757.6666666667 (the remainder is 2, so 3 is not a divisor of 5273)
...
5273 / 5272 = 1.0001896813354 (the remainder is 1, so 5272 is not a divisor of 5273)
5273 / 5273 = 1 (the remainder is 0, so 5273 is a divisor of 5273)

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 5273 (i.e. 72.615425358528). 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 $\frac{N}{d} = D$ )

5273 / 1 = 5273 (the remainder is 0, so 1 and 5273 are divisors of 5273)
5273 / 2 = 2636.5 (the remainder is 1, so 2 is not a divisor of 5273)
5273 / 3 = 1757.6666666667 (the remainder is 2, so 3 is not a divisor of 5273)
...
5273 / 71 = 74.267605633803 (the remainder is 19, so 71 is not a divisor of 5273)
5273 / 72 = 73.236111111111 (the remainder is 17, so 72 is not a divisor of 5273)