What are the divisors of 9202?

1, 2, 43, 86, 107, 214, 4601, 9202

There is a total of 8 positive divisors.
The sum of these divisors is 14256.
The arithmetic mean is 1782.

4 even divisors

2, 86, 214, 9202

4 odd divisors

1, 43, 107, 4601

How to compute the divisors of 9202?

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 9202 by each of the numbers from 1 to 9202 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)

9202 / 1 = 9202 (the remainder is 0, so 1 is a divisor of 9202)
9202 / 2 = 4601 (the remainder is 0, so 2 is a divisor of 9202)
9202 / 3 = 3067.3333333333 (the remainder is 1, so 3 is not a divisor of 9202)
...
9202 / 9201 = 1.0001086838387 (the remainder is 1, so 9201 is not a divisor of 9202)
9202 / 9202 = 1 (the remainder is 0, so 9202 is a divisor of 9202)

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 9202 (i.e. 95.927055620404). 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 $\frac{N}{d} = D$ )

9202 / 1 = 9202 (the remainder is 0, so 1 and 9202 are divisors of 9202)
9202 / 2 = 4601 (the remainder is 0, so 2 and 4601 are divisors of 9202)
9202 / 3 = 3067.3333333333 (the remainder is 1, so 3 is not a divisor of 9202)
...
9202 / 94 = 97.893617021277 (the remainder is 84, so 94 is not a divisor of 9202)
9202 / 95 = 96.863157894737 (the remainder is 82, so 95 is not a divisor of 9202)