What are the divisors of 9053?

1, 11, 823, 9053

There is a total of 4 positive divisors.
The sum of these divisors is 9888.
The arithmetic mean is 2472.

4 odd divisors

1, 11, 823, 9053

How to compute the divisors of 9053?

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 9053 by each of the numbers from 1 to 9053 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)

9053 / 1 = 9053 (the remainder is 0, so 1 is a divisor of 9053)
9053 / 2 = 4526.5 (the remainder is 1, so 2 is not a divisor of 9053)
9053 / 3 = 3017.6666666667 (the remainder is 2, so 3 is not a divisor of 9053)
...
9053 / 9052 = 1.0001104728237 (the remainder is 1, so 9052 is not a divisor of 9053)
9053 / 9053 = 1 (the remainder is 0, so 9053 is a divisor of 9053)

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 9053 (i.e. 95.147254295644). 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 $\frac{N}{d} = D$ )

9053 / 1 = 9053 (the remainder is 0, so 1 and 9053 are divisors of 9053)
9053 / 2 = 4526.5 (the remainder is 1, so 2 is not a divisor of 9053)
9053 / 3 = 3017.6666666667 (the remainder is 2, so 3 is not a divisor of 9053)
...
9053 / 94 = 96.308510638298 (the remainder is 29, so 94 is not a divisor of 9053)
9053 / 95 = 95.294736842105 (the remainder is 28, so 95 is not a divisor of 9053)