What are the divisors of 9037?

1, 7, 1291, 9037

There is a total of 4 positive divisors.
The sum of these divisors is 10336.
The arithmetic mean is 2584.

4 odd divisors

1, 7, 1291, 9037

How to compute the divisors of 9037?

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 9037 by each of the numbers from 1 to 9037 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)

9037 / 1 = 9037 (the remainder is 0, so 1 is a divisor of 9037)
9037 / 2 = 4518.5 (the remainder is 1, so 2 is not a divisor of 9037)
9037 / 3 = 3012.3333333333 (the remainder is 1, so 3 is not a divisor of 9037)
...
9037 / 9036 = 1.0001106684374 (the remainder is 1, so 9036 is not a divisor of 9037)
9037 / 9037 = 1 (the remainder is 0, so 9037 is a divisor of 9037)

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 9037 (i.e. 95.063136914369). 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 $\frac{N}{d} = D$ )

9037 / 1 = 9037 (the remainder is 0, so 1 and 9037 are divisors of 9037)
9037 / 2 = 4518.5 (the remainder is 1, so 2 is not a divisor of 9037)
9037 / 3 = 3012.3333333333 (the remainder is 1, so 3 is not a divisor of 9037)
...
9037 / 94 = 96.13829787234 (the remainder is 13, so 94 is not a divisor of 9037)
9037 / 95 = 95.126315789474 (the remainder is 12, so 95 is not a divisor of 9037)