What are the divisors of 2548?

1, 2, 4, 7, 13, 14, 26, 28, 49, 52, 91, 98, 182, 196, 364, 637, 1274, 2548

There is a total of 18 positive divisors.
The sum of these divisors is 5586.
The arithmetic mean is 310.33333333333.

12 even divisors

2, 4, 14, 26, 28, 52, 98, 182, 196, 364, 1274, 2548

6 odd divisors

1, 7, 13, 49, 91, 637

How to compute the divisors of 2548?

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 2548 by each of the numbers from 1 to 2548 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)

2548 / 1 = 2548 (the remainder is 0, so 1 is a divisor of 2548)
2548 / 2 = 1274 (the remainder is 0, so 2 is a divisor of 2548)
2548 / 3 = 849.33333333333 (the remainder is 1, so 3 is not a divisor of 2548)
...
2548 / 2547 = 1.0003926187672 (the remainder is 1, so 2547 is not a divisor of 2548)
2548 / 2548 = 1 (the remainder is 0, so 2548 is a divisor of 2548)

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 2548 (i.e. 50.477717856496). 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 $\frac{N}{d} = D$ )

2548 / 1 = 2548 (the remainder is 0, so 1 and 2548 are divisors of 2548)
2548 / 2 = 1274 (the remainder is 0, so 2 and 1274 are divisors of 2548)
2548 / 3 = 849.33333333333 (the remainder is 1, so 3 is not a divisor of 2548)
...
2548 / 49 = 52 (the remainder is 0, so 49 and 52 are divisors of 2548)
2548 / 50 = 50.96 (the remainder is 48, so 50 is not a divisor of 2548)