What are the divisors of 6046?

1, 2, 3023, 6046

There is a total of 4 positive divisors.
The sum of these divisors is 9072.
The arithmetic mean is 2268.

2 even divisors

2, 6046

2 odd divisors

1, 3023

How to compute the divisors of 6046?

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 6046 by each of the numbers from 1 to 6046 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)

6046 / 1 = 6046 (the remainder is 0, so 1 is a divisor of 6046)
6046 / 2 = 3023 (the remainder is 0, so 2 is a divisor of 6046)
6046 / 3 = 2015.3333333333 (the remainder is 1, so 3 is not a divisor of 6046)
...
6046 / 6045 = 1.0001654259719 (the remainder is 1, so 6045 is not a divisor of 6046)
6046 / 6046 = 1 (the remainder is 0, so 6046 is a divisor of 6046)

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 6046 (i.e. 77.756028705175). 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 $\frac{N}{d} = D$ )

6046 / 1 = 6046 (the remainder is 0, so 1 and 6046 are divisors of 6046)
6046 / 2 = 3023 (the remainder is 0, so 2 and 3023 are divisors of 6046)
6046 / 3 = 2015.3333333333 (the remainder is 1, so 3 is not a divisor of 6046)
...
6046 / 76 = 79.552631578947 (the remainder is 42, so 76 is not a divisor of 6046)
6046 / 77 = 78.519480519481 (the remainder is 40, so 77 is not a divisor of 6046)