What are the divisors of 2537?

1, 43, 59, 2537

There is a total of 4 positive divisors.
The sum of these divisors is 2640.
The arithmetic mean is 660.

4 odd divisors

1, 43, 59, 2537

How to compute the divisors of 2537?

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 2537 by each of the numbers from 1 to 2537 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)

2537 / 1 = 2537 (the remainder is 0, so 1 is a divisor of 2537)
2537 / 2 = 1268.5 (the remainder is 1, so 2 is not a divisor of 2537)
2537 / 3 = 845.66666666667 (the remainder is 2, so 3 is not a divisor of 2537)
...
2537 / 2536 = 1.0003943217666 (the remainder is 1, so 2536 is not a divisor of 2537)
2537 / 2537 = 1 (the remainder is 0, so 2537 is a divisor of 2537)

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 2537 (i.e. 50.368641037852). 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 $\frac{N}{d} = D$ )

2537 / 1 = 2537 (the remainder is 0, so 1 and 2537 are divisors of 2537)
2537 / 2 = 1268.5 (the remainder is 1, so 2 is not a divisor of 2537)
2537 / 3 = 845.66666666667 (the remainder is 2, so 3 is not a divisor of 2537)
...
2537 / 49 = 51.775510204082 (the remainder is 38, so 49 is not a divisor of 2537)
2537 / 50 = 50.74 (the remainder is 37, so 50 is not a divisor of 2537)