What are the divisors of 9049?

1, 9049

There is a total of 2 positive divisors.
The sum of these divisors is 9050.
The arithmetic mean is 4525.

2 odd divisors

1, 9049

How to compute the divisors of 9049?

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 9049 by each of the numbers from 1 to 9049 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)

9049 / 1 = 9049 (the remainder is 0, so 1 is a divisor of 9049)
9049 / 2 = 4524.5 (the remainder is 1, so 2 is not a divisor of 9049)
9049 / 3 = 3016.3333333333 (the remainder is 1, so 3 is not a divisor of 9049)
...
9049 / 9048 = 1.0001105216622 (the remainder is 1, so 9048 is not a divisor of 9049)
9049 / 9049 = 1 (the remainder is 0, so 9049 is a divisor of 9049)

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 9049 (i.e. 95.126231923692). 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 $\frac{N}{d} = D$ )

9049 / 1 = 9049 (the remainder is 0, so 1 and 9049 are divisors of 9049)
9049 / 2 = 4524.5 (the remainder is 1, so 2 is not a divisor of 9049)
9049 / 3 = 3016.3333333333 (the remainder is 1, so 3 is not a divisor of 9049)
...
9049 / 94 = 96.265957446809 (the remainder is 25, so 94 is not a divisor of 9049)
9049 / 95 = 95.252631578947 (the remainder is 24, so 95 is not a divisor of 9049)