What are the divisors of 2578?

1, 2, 1289, 2578

There is a total of 4 positive divisors.
The sum of these divisors is 3870.
The arithmetic mean is 967.5.

2 even divisors

2, 2578

2 odd divisors

1, 1289

How to compute the divisors of 2578?

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 2578 by each of the numbers from 1 to 2578 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)

2578 / 1 = 2578 (the remainder is 0, so 1 is a divisor of 2578)
2578 / 2 = 1289 (the remainder is 0, so 2 is a divisor of 2578)
2578 / 3 = 859.33333333333 (the remainder is 1, so 3 is not a divisor of 2578)
...
2578 / 2577 = 1.000388048118 (the remainder is 1, so 2577 is not a divisor of 2578)
2578 / 2578 = 1 (the remainder is 0, so 2578 is a divisor of 2578)

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 2578 (i.e. 50.774009099144). 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 $\frac{N}{d} = D$ )

2578 / 1 = 2578 (the remainder is 0, so 1 and 2578 are divisors of 2578)
2578 / 2 = 1289 (the remainder is 0, so 2 and 1289 are divisors of 2578)
2578 / 3 = 859.33333333333 (the remainder is 1, so 3 is not a divisor of 2578)
...
2578 / 49 = 52.612244897959 (the remainder is 30, so 49 is not a divisor of 2578)
2578 / 50 = 51.56 (the remainder is 28, so 50 is not a divisor of 2578)