What are the divisors of 3088?

1, 2, 4, 8, 16, 193, 386, 772, 1544, 3088

There is a total of 10 positive divisors.
The sum of these divisors is 6014.
The arithmetic mean is 601.4.

8 even divisors

2, 4, 8, 16, 386, 772, 1544, 3088

2 odd divisors

1, 193

How to compute the divisors of 3088?

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 3088 by each of the numbers from 1 to 3088 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)

3088 / 1 = 3088 (the remainder is 0, so 1 is a divisor of 3088)
3088 / 2 = 1544 (the remainder is 0, so 2 is a divisor of 3088)
3088 / 3 = 1029.3333333333 (the remainder is 1, so 3 is not a divisor of 3088)
...
3088 / 3087 = 1.0003239390994 (the remainder is 1, so 3087 is not a divisor of 3088)
3088 / 3088 = 1 (the remainder is 0, so 3088 is a divisor of 3088)

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 3088 (i.e. 55.569775957799). 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 $\frac{N}{d} = D$ )

3088 / 1 = 3088 (the remainder is 0, so 1 and 3088 are divisors of 3088)
3088 / 2 = 1544 (the remainder is 0, so 2 and 1544 are divisors of 3088)
3088 / 3 = 1029.3333333333 (the remainder is 1, so 3 is not a divisor of 3088)
...
3088 / 54 = 57.185185185185 (the remainder is 10, so 54 is not a divisor of 3088)
3088 / 55 = 56.145454545455 (the remainder is 8, so 55 is not a divisor of 3088)