What are the divisors of 9026?

1, 2, 4513, 9026

There is a total of 4 positive divisors.
The sum of these divisors is 13542.
The arithmetic mean is 3385.5.

2 even divisors

2, 9026

2 odd divisors

1, 4513

How to compute the divisors of 9026?

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 9026 by each of the numbers from 1 to 9026 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)

9026 / 1 = 9026 (the remainder is 0, so 1 is a divisor of 9026)
9026 / 2 = 4513 (the remainder is 0, so 2 is a divisor of 9026)
9026 / 3 = 3008.6666666667 (the remainder is 2, so 3 is not a divisor of 9026)
...
9026 / 9025 = 1.0001108033241 (the remainder is 1, so 9025 is not a divisor of 9026)
9026 / 9026 = 1 (the remainder is 0, so 9026 is a divisor of 9026)

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 9026 (i.e. 95.005263012109). 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 $\frac{N}{d} = D$ )

9026 / 1 = 9026 (the remainder is 0, so 1 and 9026 are divisors of 9026)
9026 / 2 = 4513 (the remainder is 0, so 2 and 4513 are divisors of 9026)
9026 / 3 = 3008.6666666667 (the remainder is 2, so 3 is not a divisor of 9026)
...
9026 / 94 = 96.021276595745 (the remainder is 2, so 94 is not a divisor of 9026)
9026 / 95 = 95.010526315789 (the remainder is 1, so 95 is not a divisor of 9026)