What are the divisors of 2562?

1, 2, 3, 6, 7, 14, 21, 42, 61, 122, 183, 366, 427, 854, 1281, 2562

There is a total of 16 positive divisors.
The sum of these divisors is 5952.
The arithmetic mean is 372.

8 even divisors

2, 6, 14, 42, 122, 366, 854, 2562

8 odd divisors

1, 3, 7, 21, 61, 183, 427, 1281

How to compute the divisors of 2562?

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 2562 by each of the numbers from 1 to 2562 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)

2562 / 1 = 2562 (the remainder is 0, so 1 is a divisor of 2562)
2562 / 2 = 1281 (the remainder is 0, so 2 is a divisor of 2562)
2562 / 3 = 854 (the remainder is 0, so 3 is a divisor of 2562)
...
2562 / 2561 = 1.0003904724717 (the remainder is 1, so 2561 is not a divisor of 2562)
2562 / 2562 = 1 (the remainder is 0, so 2562 is a divisor of 2562)

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 2562 (i.e. 50.616202939375). 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 $\frac{N}{d} = D$ )

2562 / 1 = 2562 (the remainder is 0, so 1 and 2562 are divisors of 2562)
2562 / 2 = 1281 (the remainder is 0, so 2 and 1281 are divisors of 2562)
2562 / 3 = 854 (the remainder is 0, so 3 and 854 are divisors of 2562)
...
2562 / 49 = 52.285714285714 (the remainder is 14, so 49 is not a divisor of 2562)
2562 / 50 = 51.24 (the remainder is 12, so 50 is not a divisor of 2562)