What are the divisors of 9028?

1, 2, 4, 37, 61, 74, 122, 148, 244, 2257, 4514, 9028

There is a total of 12 positive divisors.
The sum of these divisors is 16492.
The arithmetic mean is 1374.3333333333.

8 even divisors

2, 4, 74, 122, 148, 244, 4514, 9028

4 odd divisors

1, 37, 61, 2257

How to compute the divisors of 9028?

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 9028 by each of the numbers from 1 to 9028 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)

9028 / 1 = 9028 (the remainder is 0, so 1 is a divisor of 9028)
9028 / 2 = 4514 (the remainder is 0, so 2 is a divisor of 9028)
9028 / 3 = 3009.3333333333 (the remainder is 1, so 3 is not a divisor of 9028)
...
9028 / 9027 = 1.0001107787748 (the remainder is 1, so 9027 is not a divisor of 9028)
9028 / 9028 = 1 (the remainder is 0, so 9028 is a divisor of 9028)

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 9028 (i.e. 95.015788161758). 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 $\frac{N}{d} = D$ )

9028 / 1 = 9028 (the remainder is 0, so 1 and 9028 are divisors of 9028)
9028 / 2 = 4514 (the remainder is 0, so 2 and 4514 are divisors of 9028)
9028 / 3 = 3009.3333333333 (the remainder is 1, so 3 is not a divisor of 9028)
...
9028 / 94 = 96.042553191489 (the remainder is 4, so 94 is not a divisor of 9028)
9028 / 95 = 95.031578947368 (the remainder is 3, so 95 is not a divisor of 9028)