What are the divisors of 2192?

1, 2, 4, 8, 16, 137, 274, 548, 1096, 2192

There is a total of 10 positive divisors.
The sum of these divisors is 4278.
The arithmetic mean is 427.8.

8 even divisors

2, 4, 8, 16, 274, 548, 1096, 2192

2 odd divisors

1, 137

How to compute the divisors of 2192?

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 2192 by each of the numbers from 1 to 2192 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)

2192 / 1 = 2192 (the remainder is 0, so 1 is a divisor of 2192)
2192 / 2 = 1096 (the remainder is 0, so 2 is a divisor of 2192)
2192 / 3 = 730.66666666667 (the remainder is 2, so 3 is not a divisor of 2192)
...
2192 / 2191 = 1.000456412597 (the remainder is 1, so 2191 is not a divisor of 2192)
2192 / 2192 = 1 (the remainder is 0, so 2192 is a divisor of 2192)

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 2192 (i.e. 46.818799642879). 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 $\frac{N}{d} = D$ )

2192 / 1 = 2192 (the remainder is 0, so 1 and 2192 are divisors of 2192)
2192 / 2 = 1096 (the remainder is 0, so 2 and 1096 are divisors of 2192)
2192 / 3 = 730.66666666667 (the remainder is 2, so 3 is not a divisor of 2192)
...
2192 / 45 = 48.711111111111 (the remainder is 32, so 45 is not a divisor of 2192)
2192 / 46 = 47.652173913043 (the remainder is 30, so 46 is not a divisor of 2192)