What are the divisors of 9077?

1, 29, 313, 9077

There is a total of 4 positive divisors.
The sum of these divisors is 9420.
The arithmetic mean is 2355.

4 odd divisors

1, 29, 313, 9077

How to compute the divisors of 9077?

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 9077 by each of the numbers from 1 to 9077 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)

9077 / 1 = 9077 (the remainder is 0, so 1 is a divisor of 9077)
9077 / 2 = 4538.5 (the remainder is 1, so 2 is not a divisor of 9077)
9077 / 3 = 3025.6666666667 (the remainder is 2, so 3 is not a divisor of 9077)
...
9077 / 9076 = 1.0001101806963 (the remainder is 1, so 9076 is not a divisor of 9077)
9077 / 9077 = 1 (the remainder is 0, so 9077 is a divisor of 9077)

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 9077 (i.e. 95.273291115611). 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 $\frac{N}{d} = D$ )

9077 / 1 = 9077 (the remainder is 0, so 1 and 9077 are divisors of 9077)
9077 / 2 = 4538.5 (the remainder is 1, so 2 is not a divisor of 9077)
9077 / 3 = 3025.6666666667 (the remainder is 2, so 3 is not a divisor of 9077)
...
9077 / 94 = 96.563829787234 (the remainder is 53, so 94 is not a divisor of 9077)
9077 / 95 = 95.547368421053 (the remainder is 52, so 95 is not a divisor of 9077)