What are the divisors of 9070?

1, 2, 5, 10, 907, 1814, 4535, 9070

There is a total of 8 positive divisors.
The sum of these divisors is 16344.
The arithmetic mean is 2043.

4 even divisors

2, 10, 1814, 9070

4 odd divisors

1, 5, 907, 4535

How to compute the divisors of 9070?

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 9070 by each of the numbers from 1 to 9070 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)

9070 / 1 = 9070 (the remainder is 0, so 1 is a divisor of 9070)
9070 / 2 = 4535 (the remainder is 0, so 2 is a divisor of 9070)
9070 / 3 = 3023.3333333333 (the remainder is 1, so 3 is not a divisor of 9070)
...
9070 / 9069 = 1.0001102657404 (the remainder is 1, so 9069 is not a divisor of 9070)
9070 / 9070 = 1 (the remainder is 0, so 9070 is a divisor of 9070)

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 9070 (i.e. 95.236547606473). 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 $\frac{N}{d} = D$ )

9070 / 1 = 9070 (the remainder is 0, so 1 and 9070 are divisors of 9070)
9070 / 2 = 4535 (the remainder is 0, so 2 and 4535 are divisors of 9070)
9070 / 3 = 3023.3333333333 (the remainder is 1, so 3 is not a divisor of 9070)
...
9070 / 94 = 96.489361702128 (the remainder is 46, so 94 is not a divisor of 9070)
9070 / 95 = 95.473684210526 (the remainder is 45, so 95 is not a divisor of 9070)