What are the divisors of 3047?

1, 11, 277, 3047

There is a total of 4 positive divisors.
The sum of these divisors is 3336.
The arithmetic mean is 834.

4 odd divisors

1, 11, 277, 3047

How to compute the divisors of 3047?

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 3047 by each of the numbers from 1 to 3047 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)

3047 / 1 = 3047 (the remainder is 0, so 1 is a divisor of 3047)
3047 / 2 = 1523.5 (the remainder is 1, so 2 is not a divisor of 3047)
3047 / 3 = 1015.6666666667 (the remainder is 2, so 3 is not a divisor of 3047)
...
3047 / 3046 = 1.0003282994091 (the remainder is 1, so 3046 is not a divisor of 3047)
3047 / 3047 = 1 (the remainder is 0, so 3047 is a divisor of 3047)

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 3047 (i.e. 55.19963767997). 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 $\frac{N}{d} = D$ )

3047 / 1 = 3047 (the remainder is 0, so 1 and 3047 are divisors of 3047)
3047 / 2 = 1523.5 (the remainder is 1, so 2 is not a divisor of 3047)
3047 / 3 = 1015.6666666667 (the remainder is 2, so 3 is not a divisor of 3047)
...
3047 / 54 = 56.425925925926 (the remainder is 23, so 54 is not a divisor of 3047)
3047 / 55 = 55.4 (the remainder is 22, so 55 is not a divisor of 3047)