What are the divisors of 3092?

1, 2, 4, 773, 1546, 3092

There is a total of 6 positive divisors.
The sum of these divisors is 5418.
The arithmetic mean is 903.

4 even divisors

2, 4, 1546, 3092

2 odd divisors

1, 773

How to compute the divisors of 3092?

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 3092 by each of the numbers from 1 to 3092 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)

3092 / 1 = 3092 (the remainder is 0, so 1 is a divisor of 3092)
3092 / 2 = 1546 (the remainder is 0, so 2 is a divisor of 3092)
3092 / 3 = 1030.6666666667 (the remainder is 2, so 3 is not a divisor of 3092)
...
3092 / 3091 = 1.0003235198965 (the remainder is 1, so 3091 is not a divisor of 3092)
3092 / 3092 = 1 (the remainder is 0, so 3092 is a divisor of 3092)

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 3092 (i.e. 55.605755097831). 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 $\frac{N}{d} = D$ )

3092 / 1 = 3092 (the remainder is 0, so 1 and 3092 are divisors of 3092)
3092 / 2 = 1546 (the remainder is 0, so 2 and 1546 are divisors of 3092)
3092 / 3 = 1030.6666666667 (the remainder is 2, so 3 is not a divisor of 3092)
...
3092 / 54 = 57.259259259259 (the remainder is 14, so 54 is not a divisor of 3092)
3092 / 55 = 56.218181818182 (the remainder is 12, so 55 is not a divisor of 3092)