What are the divisors of 4192?

1, 2, 4, 8, 16, 32, 131, 262, 524, 1048, 2096, 4192

There is a total of 12 positive divisors.
The sum of these divisors is 8316.
The arithmetic mean is 693.

10 even divisors

2, 4, 8, 16, 32, 262, 524, 1048, 2096, 4192

2 odd divisors

1, 131

How to compute the divisors of 4192?

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 4192 by each of the numbers from 1 to 4192 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)

4192 / 1 = 4192 (the remainder is 0, so 1 is a divisor of 4192)
4192 / 2 = 2096 (the remainder is 0, so 2 is a divisor of 4192)
4192 / 3 = 1397.3333333333 (the remainder is 1, so 3 is not a divisor of 4192)
...
4192 / 4191 = 1.0002386065378 (the remainder is 1, so 4191 is not a divisor of 4192)
4192 / 4192 = 1 (the remainder is 0, so 4192 is a divisor of 4192)

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 4192 (i.e. 64.745656224955). 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 $\frac{N}{d} = D$ )

4192 / 1 = 4192 (the remainder is 0, so 1 and 4192 are divisors of 4192)
4192 / 2 = 2096 (the remainder is 0, so 2 and 2096 are divisors of 4192)
4192 / 3 = 1397.3333333333 (the remainder is 1, so 3 is not a divisor of 4192)
...
4192 / 63 = 66.539682539683 (the remainder is 34, so 63 is not a divisor of 4192)
4192 / 64 = 65.5 (the remainder is 32, so 64 is not a divisor of 4192)