What are the divisors of 9041?

1, 9041

There is a total of 2 positive divisors.
The sum of these divisors is 9042.
The arithmetic mean is 4521.

2 odd divisors

1, 9041

How to compute the divisors of 9041?

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 9041 by each of the numbers from 1 to 9041 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)

9041 / 1 = 9041 (the remainder is 0, so 1 is a divisor of 9041)
9041 / 2 = 4520.5 (the remainder is 1, so 2 is not a divisor of 9041)
9041 / 3 = 3013.6666666667 (the remainder is 2, so 3 is not a divisor of 9041)
...
9041 / 9040 = 1.000110619469 (the remainder is 1, so 9040 is not a divisor of 9041)
9041 / 9041 = 1 (the remainder is 0, so 9041 is a divisor of 9041)

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 9041 (i.e. 95.084173236139). 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 $\frac{N}{d} = D$ )

9041 / 1 = 9041 (the remainder is 0, so 1 and 9041 are divisors of 9041)
9041 / 2 = 4520.5 (the remainder is 1, so 2 is not a divisor of 9041)
9041 / 3 = 3013.6666666667 (the remainder is 2, so 3 is not a divisor of 9041)
...
9041 / 94 = 96.18085106383 (the remainder is 17, so 94 is not a divisor of 9041)
9041 / 95 = 95.168421052632 (the remainder is 16, so 95 is not a divisor of 9041)