What are the divisors of 9088?

1, 2, 4, 8, 16, 32, 64, 71, 128, 142, 284, 568, 1136, 2272, 4544, 9088

There is a total of 16 positive divisors.
The sum of these divisors is 18360.
The arithmetic mean is 1147.5.

14 even divisors

2, 4, 8, 16, 32, 64, 128, 142, 284, 568, 1136, 2272, 4544, 9088

2 odd divisors

1, 71

How to compute the divisors of 9088?

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 9088 by each of the numbers from 1 to 9088 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)

9088 / 1 = 9088 (the remainder is 0, so 1 is a divisor of 9088)
9088 / 2 = 4544 (the remainder is 0, so 2 is a divisor of 9088)
9088 / 3 = 3029.3333333333 (the remainder is 1, so 3 is not a divisor of 9088)
...
9088 / 9087 = 1.0001100473203 (the remainder is 1, so 9087 is not a divisor of 9088)
9088 / 9088 = 1 (the remainder is 0, so 9088 is a divisor of 9088)

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 9088 (i.e. 95.331002302504). 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 $\frac{N}{d} = D$ )

9088 / 1 = 9088 (the remainder is 0, so 1 and 9088 are divisors of 9088)
9088 / 2 = 4544 (the remainder is 0, so 2 and 4544 are divisors of 9088)
9088 / 3 = 3029.3333333333 (the remainder is 1, so 3 is not a divisor of 9088)
...
9088 / 94 = 96.68085106383 (the remainder is 64, so 94 is not a divisor of 9088)
9088 / 95 = 95.663157894737 (the remainder is 63, so 95 is not a divisor of 9088)