What are the divisors of 9222?

1, 2, 3, 6, 29, 53, 58, 87, 106, 159, 174, 318, 1537, 3074, 4611, 9222

There is a total of 16 positive divisors.
The sum of these divisors is 19440.
The arithmetic mean is 1215.

8 even divisors

2, 6, 58, 106, 174, 318, 3074, 9222

8 odd divisors

1, 3, 29, 53, 87, 159, 1537, 4611

How to compute the divisors of 9222?

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 9222 by each of the numbers from 1 to 9222 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)

9222 / 1 = 9222 (the remainder is 0, so 1 is a divisor of 9222)
9222 / 2 = 4611 (the remainder is 0, so 2 is a divisor of 9222)
9222 / 3 = 3074 (the remainder is 0, so 3 is a divisor of 9222)
...
9222 / 9221 = 1.0001084481076 (the remainder is 1, so 9221 is not a divisor of 9222)
9222 / 9222 = 1 (the remainder is 0, so 9222 is a divisor of 9222)

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 9222 (i.e. 96.031244915392). 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 $\frac{N}{d} = D$ )

9222 / 1 = 9222 (the remainder is 0, so 1 and 9222 are divisors of 9222)
9222 / 2 = 4611 (the remainder is 0, so 2 and 4611 are divisors of 9222)
9222 / 3 = 3074 (the remainder is 0, so 3 and 3074 are divisors of 9222)
...
9222 / 95 = 97.073684210526 (the remainder is 7, so 95 is not a divisor of 9222)
9222 / 96 = 96.0625 (the remainder is 6, so 96 is not a divisor of 9222)