What are the divisors of 7088?

1, 2, 4, 8, 16, 443, 886, 1772, 3544, 7088

There is a total of 10 positive divisors.
The sum of these divisors is 13764.
The arithmetic mean is 1376.4.

8 even divisors

2, 4, 8, 16, 886, 1772, 3544, 7088

2 odd divisors

1, 443

How to compute the divisors of 7088?

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 7088 by each of the numbers from 1 to 7088 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)

7088 / 1 = 7088 (the remainder is 0, so 1 is a divisor of 7088)
7088 / 2 = 3544 (the remainder is 0, so 2 is a divisor of 7088)
7088 / 3 = 2362.6666666667 (the remainder is 2, so 3 is not a divisor of 7088)
...
7088 / 7087 = 1.0001411034288 (the remainder is 1, so 7087 is not a divisor of 7088)
7088 / 7088 = 1 (the remainder is 0, so 7088 is a divisor of 7088)

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 7088 (i.e. 84.190260719397). 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 $\frac{N}{d} = D$ )

7088 / 1 = 7088 (the remainder is 0, so 1 and 7088 are divisors of 7088)
7088 / 2 = 3544 (the remainder is 0, so 2 and 3544 are divisors of 7088)
7088 / 3 = 2362.6666666667 (the remainder is 2, so 3 is not a divisor of 7088)
...
7088 / 83 = 85.397590361446 (the remainder is 33, so 83 is not a divisor of 7088)
7088 / 84 = 84.380952380952 (the remainder is 32, so 84 is not a divisor of 7088)