What are the divisors of 5257?

1, 7, 751, 5257

There is a total of 4 positive divisors.
The sum of these divisors is 6016.
The arithmetic mean is 1504.

4 odd divisors

1, 7, 751, 5257

How to compute the divisors of 5257?

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 5257 by each of the numbers from 1 to 5257 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)

5257 / 1 = 5257 (the remainder is 0, so 1 is a divisor of 5257)
5257 / 2 = 2628.5 (the remainder is 1, so 2 is not a divisor of 5257)
5257 / 3 = 1752.3333333333 (the remainder is 1, so 3 is not a divisor of 5257)
...
5257 / 5256 = 1.0001902587519 (the remainder is 1, so 5256 is not a divisor of 5257)
5257 / 5257 = 1 (the remainder is 0, so 5257 is a divisor of 5257)

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 5257 (i.e. 72.505172229297). 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 $\frac{N}{d} = D$ )

5257 / 1 = 5257 (the remainder is 0, so 1 and 5257 are divisors of 5257)
5257 / 2 = 2628.5 (the remainder is 1, so 2 is not a divisor of 5257)
5257 / 3 = 1752.3333333333 (the remainder is 1, so 3 is not a divisor of 5257)
...
5257 / 71 = 74.042253521127 (the remainder is 3, so 71 is not a divisor of 5257)
5257 / 72 = 73.013888888889 (the remainder is 1, so 72 is not a divisor of 5257)