What are the divisors of 6088?

1, 2, 4, 8, 761, 1522, 3044, 6088

There is a total of 8 positive divisors.
The sum of these divisors is 11430.
The arithmetic mean is 1428.75.

6 even divisors

2, 4, 8, 1522, 3044, 6088

2 odd divisors

1, 761

How to compute the divisors of 6088?

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 6088 by each of the numbers from 1 to 6088 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)

6088 / 1 = 6088 (the remainder is 0, so 1 is a divisor of 6088)
6088 / 2 = 3044 (the remainder is 0, so 2 is a divisor of 6088)
6088 / 3 = 2029.3333333333 (the remainder is 1, so 3 is not a divisor of 6088)
...
6088 / 6087 = 1.0001642845408 (the remainder is 1, so 6087 is not a divisor of 6088)
6088 / 6088 = 1 (the remainder is 0, so 6088 is a divisor of 6088)

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 6088 (i.e. 78.025636812525). 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 $\frac{N}{d} = D$ )

6088 / 1 = 6088 (the remainder is 0, so 1 and 6088 are divisors of 6088)
6088 / 2 = 3044 (the remainder is 0, so 2 and 3044 are divisors of 6088)
6088 / 3 = 2029.3333333333 (the remainder is 1, so 3 is not a divisor of 6088)
...
6088 / 77 = 79.064935064935 (the remainder is 5, so 77 is not a divisor of 6088)
6088 / 78 = 78.051282051282 (the remainder is 4, so 78 is not a divisor of 6088)