What are the divisors of 2531?

1, 2531

There is a total of 2 positive divisors.
The sum of these divisors is 2532.
The arithmetic mean is 1266.

2 odd divisors

1, 2531

How to compute the divisors of 2531?

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 2531 by each of the numbers from 1 to 2531 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)

2531 / 1 = 2531 (the remainder is 0, so 1 is a divisor of 2531)
2531 / 2 = 1265.5 (the remainder is 1, so 2 is not a divisor of 2531)
2531 / 3 = 843.66666666667 (the remainder is 2, so 3 is not a divisor of 2531)
...
2531 / 2530 = 1.000395256917 (the remainder is 1, so 2530 is not a divisor of 2531)
2531 / 2531 = 1 (the remainder is 0, so 2531 is a divisor of 2531)

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 2531 (i.e. 50.309044912421). 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 $\frac{N}{d} = D$ )

2531 / 1 = 2531 (the remainder is 0, so 1 and 2531 are divisors of 2531)
2531 / 2 = 1265.5 (the remainder is 1, so 2 is not a divisor of 2531)
2531 / 3 = 843.66666666667 (the remainder is 2, so 3 is not a divisor of 2531)
...
2531 / 49 = 51.65306122449 (the remainder is 32, so 49 is not a divisor of 2531)
2531 / 50 = 50.62 (the remainder is 31, so 50 is not a divisor of 2531)