What are the divisors of 9214?

1, 2, 17, 34, 271, 542, 4607, 9214

There is a total of 8 positive divisors.
The sum of these divisors is 14688.
The arithmetic mean is 1836.

4 even divisors

2, 34, 542, 9214

4 odd divisors

1, 17, 271, 4607

How to compute the divisors of 9214?

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 9214 by each of the numbers from 1 to 9214 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)

9214 / 1 = 9214 (the remainder is 0, so 1 is a divisor of 9214)
9214 / 2 = 4607 (the remainder is 0, so 2 is a divisor of 9214)
9214 / 3 = 3071.3333333333 (the remainder is 1, so 3 is not a divisor of 9214)
...
9214 / 9213 = 1.0001085422772 (the remainder is 1, so 9213 is not a divisor of 9214)
9214 / 9214 = 1 (the remainder is 0, so 9214 is a divisor of 9214)

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 9214 (i.e. 95.989582768132). 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 $\frac{N}{d} = D$ )

9214 / 1 = 9214 (the remainder is 0, so 1 and 9214 are divisors of 9214)
9214 / 2 = 4607 (the remainder is 0, so 2 and 4607 are divisors of 9214)
9214 / 3 = 3071.3333333333 (the remainder is 1, so 3 is not a divisor of 9214)
...
9214 / 94 = 98.021276595745 (the remainder is 2, so 94 is not a divisor of 9214)
9214 / 95 = 96.989473684211 (the remainder is 94, so 95 is not a divisor of 9214)