What are the divisors of 9583?

1, 7, 37, 259, 1369, 9583

There is a total of 6 positive divisors.
The sum of these divisors is 11256.
The arithmetic mean is 1876.

6 odd divisors

1, 7, 37, 259, 1369, 9583

How to compute the divisors of 9583?

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 9583 by each of the numbers from 1 to 9583 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)

9583 / 1 = 9583 (the remainder is 0, so 1 is a divisor of 9583)
9583 / 2 = 4791.5 (the remainder is 1, so 2 is not a divisor of 9583)
9583 / 3 = 3194.3333333333 (the remainder is 1, so 3 is not a divisor of 9583)
...
9583 / 9582 = 1.0001043623461 (the remainder is 1, so 9582 is not a divisor of 9583)
9583 / 9583 = 1 (the remainder is 0, so 9583 is a divisor of 9583)

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 9583 (i.e. 97.89279850939). 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 $\frac{N}{d} = D$ )

9583 / 1 = 9583 (the remainder is 0, so 1 and 9583 are divisors of 9583)
9583 / 2 = 4791.5 (the remainder is 1, so 2 is not a divisor of 9583)
9583 / 3 = 3194.3333333333 (the remainder is 1, so 3 is not a divisor of 9583)
...
9583 / 96 = 99.822916666667 (the remainder is 79, so 96 is not a divisor of 9583)
9583 / 97 = 98.79381443299 (the remainder is 77, so 97 is not a divisor of 9583)