What are the divisors of 9074?

1, 2, 13, 26, 349, 698, 4537, 9074

There is a total of 8 positive divisors.
The sum of these divisors is 14700.
The arithmetic mean is 1837.5.

4 even divisors

2, 26, 698, 9074

4 odd divisors

1, 13, 349, 4537

How to compute the divisors of 9074?

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 9074 by each of the numbers from 1 to 9074 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)

9074 / 1 = 9074 (the remainder is 0, so 1 is a divisor of 9074)
9074 / 2 = 4537 (the remainder is 0, so 2 is a divisor of 9074)
9074 / 3 = 3024.6666666667 (the remainder is 2, so 3 is not a divisor of 9074)
...
9074 / 9073 = 1.0001102171277 (the remainder is 1, so 9073 is not a divisor of 9074)
9074 / 9074 = 1 (the remainder is 0, so 9074 is a divisor of 9074)

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 9074 (i.e. 95.257545632879). 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 $\frac{N}{d} = D$ )

9074 / 1 = 9074 (the remainder is 0, so 1 and 9074 are divisors of 9074)
9074 / 2 = 4537 (the remainder is 0, so 2 and 4537 are divisors of 9074)
9074 / 3 = 3024.6666666667 (the remainder is 2, so 3 is not a divisor of 9074)
...
9074 / 94 = 96.531914893617 (the remainder is 50, so 94 is not a divisor of 9074)
9074 / 95 = 95.515789473684 (the remainder is 49, so 95 is not a divisor of 9074)