What are the divisors of 9035?

1, 5, 13, 65, 139, 695, 1807, 9035

There is a total of 8 positive divisors.
The sum of these divisors is 11760.
The arithmetic mean is 1470.

8 odd divisors

1, 5, 13, 65, 139, 695, 1807, 9035

How to compute the divisors of 9035?

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 9035 by each of the numbers from 1 to 9035 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)

9035 / 1 = 9035 (the remainder is 0, so 1 is a divisor of 9035)
9035 / 2 = 4517.5 (the remainder is 1, so 2 is not a divisor of 9035)
9035 / 3 = 3011.6666666667 (the remainder is 2, so 3 is not a divisor of 9035)
...
9035 / 9034 = 1.0001106929378 (the remainder is 1, so 9034 is not a divisor of 9035)
9035 / 9035 = 1 (the remainder is 0, so 9035 is a divisor of 9035)

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 9035 (i.e. 95.052617007634). 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 $\frac{N}{d} = D$ )

9035 / 1 = 9035 (the remainder is 0, so 1 and 9035 are divisors of 9035)
9035 / 2 = 4517.5 (the remainder is 1, so 2 is not a divisor of 9035)
9035 / 3 = 3011.6666666667 (the remainder is 2, so 3 is not a divisor of 9035)
...
9035 / 94 = 96.117021276596 (the remainder is 11, so 94 is not a divisor of 9035)
9035 / 95 = 95.105263157895 (the remainder is 10, so 95 is not a divisor of 9035)