What are the divisors of 3046?

1, 2, 1523, 3046

There is a total of 4 positive divisors.
The sum of these divisors is 4572.
The arithmetic mean is 1143.

2 even divisors

2, 3046

2 odd divisors

1, 1523

How to compute the divisors of 3046?

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 3046 by each of the numbers from 1 to 3046 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)

3046 / 1 = 3046 (the remainder is 0, so 1 is a divisor of 3046)
3046 / 2 = 1523 (the remainder is 0, so 2 is a divisor of 3046)
3046 / 3 = 1015.3333333333 (the remainder is 1, so 3 is not a divisor of 3046)
...
3046 / 3045 = 1.000328407225 (the remainder is 1, so 3045 is not a divisor of 3046)
3046 / 3046 = 1 (the remainder is 0, so 3046 is a divisor of 3046)

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 3046 (i.e. 55.190578906187). 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 $\frac{N}{d} = D$ )

3046 / 1 = 3046 (the remainder is 0, so 1 and 3046 are divisors of 3046)
3046 / 2 = 1523 (the remainder is 0, so 2 and 1523 are divisors of 3046)
3046 / 3 = 1015.3333333333 (the remainder is 1, so 3 is not a divisor of 3046)
...
3046 / 54 = 56.407407407407 (the remainder is 22, so 54 is not a divisor of 3046)
3046 / 55 = 55.381818181818 (the remainder is 21, so 55 is not a divisor of 3046)