What are the divisors of 2534?

1, 2, 7, 14, 181, 362, 1267, 2534

There is a total of 8 positive divisors.
The sum of these divisors is 4368.
The arithmetic mean is 546.

4 even divisors

2, 14, 362, 2534

4 odd divisors

1, 7, 181, 1267

How to compute the divisors of 2534?

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 2534 by each of the numbers from 1 to 2534 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)

2534 / 1 = 2534 (the remainder is 0, so 1 is a divisor of 2534)
2534 / 2 = 1267 (the remainder is 0, so 2 is a divisor of 2534)
2534 / 3 = 844.66666666667 (the remainder is 2, so 3 is not a divisor of 2534)
...
2534 / 2533 = 1.000394788788 (the remainder is 1, so 2533 is not a divisor of 2534)
2534 / 2534 = 1 (the remainder is 0, so 2534 is a divisor of 2534)

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 2534 (i.e. 50.338851794613). 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 $\frac{N}{d} = D$ )

2534 / 1 = 2534 (the remainder is 0, so 1 and 2534 are divisors of 2534)
2534 / 2 = 1267 (the remainder is 0, so 2 and 1267 are divisors of 2534)
2534 / 3 = 844.66666666667 (the remainder is 2, so 3 is not a divisor of 2534)
...
2534 / 49 = 51.714285714286 (the remainder is 35, so 49 is not a divisor of 2534)
2534 / 50 = 50.68 (the remainder is 34, so 50 is not a divisor of 2534)