What are the divisors of 9190?

1, 2, 5, 10, 919, 1838, 4595, 9190

There is a total of 8 positive divisors.
The sum of these divisors is 16560.
The arithmetic mean is 2070.

4 even divisors

2, 10, 1838, 9190

4 odd divisors

1, 5, 919, 4595

How to compute the divisors of 9190?

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 9190 by each of the numbers from 1 to 9190 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)

9190 / 1 = 9190 (the remainder is 0, so 1 is a divisor of 9190)
9190 / 2 = 4595 (the remainder is 0, so 2 is a divisor of 9190)
9190 / 3 = 3063.3333333333 (the remainder is 1, so 3 is not a divisor of 9190)
...
9190 / 9189 = 1.0001088257699 (the remainder is 1, so 9189 is not a divisor of 9190)
9190 / 9190 = 1 (the remainder is 0, so 9190 is a divisor of 9190)

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 9190 (i.e. 95.864487689655). 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 $\frac{N}{d} = D$ )

9190 / 1 = 9190 (the remainder is 0, so 1 and 9190 are divisors of 9190)
9190 / 2 = 4595 (the remainder is 0, so 2 and 4595 are divisors of 9190)
9190 / 3 = 3063.3333333333 (the remainder is 1, so 3 is not a divisor of 9190)
...
9190 / 94 = 97.765957446809 (the remainder is 72, so 94 is not a divisor of 9190)
9190 / 95 = 96.736842105263 (the remainder is 70, so 95 is not a divisor of 9190)