What are the divisors of 9052?

1, 2, 4, 31, 62, 73, 124, 146, 292, 2263, 4526, 9052

There is a total of 12 positive divisors.
The sum of these divisors is 16576.
The arithmetic mean is 1381.3333333333.

8 even divisors

2, 4, 62, 124, 146, 292, 4526, 9052

4 odd divisors

1, 31, 73, 2263

How to compute the divisors of 9052?

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 9052 by each of the numbers from 1 to 9052 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)

9052 / 1 = 9052 (the remainder is 0, so 1 is a divisor of 9052)
9052 / 2 = 4526 (the remainder is 0, so 2 is a divisor of 9052)
9052 / 3 = 3017.3333333333 (the remainder is 1, so 3 is not a divisor of 9052)
...
9052 / 9051 = 1.0001104850293 (the remainder is 1, so 9051 is not a divisor of 9052)
9052 / 9052 = 1 (the remainder is 0, so 9052 is a divisor of 9052)

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 9052 (i.e. 95.14199913813). 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 $\frac{N}{d} = D$ )

9052 / 1 = 9052 (the remainder is 0, so 1 and 9052 are divisors of 9052)
9052 / 2 = 4526 (the remainder is 0, so 2 and 4526 are divisors of 9052)
9052 / 3 = 3017.3333333333 (the remainder is 1, so 3 is not a divisor of 9052)
...
9052 / 94 = 96.297872340426 (the remainder is 28, so 94 is not a divisor of 9052)
9052 / 95 = 95.284210526316 (the remainder is 27, so 95 is not a divisor of 9052)