What are the divisors of 9079?

1, 7, 1297, 9079

There is a total of 4 positive divisors.
The sum of these divisors is 10384.
The arithmetic mean is 2596.

4 odd divisors

1, 7, 1297, 9079

How to compute the divisors of 9079?

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 9079 by each of the numbers from 1 to 9079 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)

9079 / 1 = 9079 (the remainder is 0, so 1 is a divisor of 9079)
9079 / 2 = 4539.5 (the remainder is 1, so 2 is not a divisor of 9079)
9079 / 3 = 3026.3333333333 (the remainder is 1, so 3 is not a divisor of 9079)
...
9079 / 9078 = 1.0001101564221 (the remainder is 1, so 9078 is not a divisor of 9079)
9079 / 9079 = 1 (the remainder is 0, so 9079 is a divisor of 9079)

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 9079 (i.e. 95.283786658592). 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 $\frac{N}{d} = D$ )

9079 / 1 = 9079 (the remainder is 0, so 1 and 9079 are divisors of 9079)
9079 / 2 = 4539.5 (the remainder is 1, so 2 is not a divisor of 9079)
9079 / 3 = 3026.3333333333 (the remainder is 1, so 3 is not a divisor of 9079)
...
9079 / 94 = 96.585106382979 (the remainder is 55, so 94 is not a divisor of 9079)
9079 / 95 = 95.568421052632 (the remainder is 54, so 95 is not a divisor of 9079)