What are the divisors of 3077?

1, 17, 181, 3077

There is a total of 4 positive divisors.
The sum of these divisors is 3276.
The arithmetic mean is 819.

4 odd divisors

1, 17, 181, 3077

How to compute the divisors of 3077?

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 3077 by each of the numbers from 1 to 3077 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)

3077 / 1 = 3077 (the remainder is 0, so 1 is a divisor of 3077)
3077 / 2 = 1538.5 (the remainder is 1, so 2 is not a divisor of 3077)
3077 / 3 = 1025.6666666667 (the remainder is 2, so 3 is not a divisor of 3077)
...
3077 / 3076 = 1.0003250975293 (the remainder is 1, so 3076 is not a divisor of 3077)
3077 / 3077 = 1 (the remainder is 0, so 3077 is a divisor of 3077)

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 3077 (i.e. 55.470712993435). 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 $\frac{N}{d} = D$ )

3077 / 1 = 3077 (the remainder is 0, so 1 and 3077 are divisors of 3077)
3077 / 2 = 1538.5 (the remainder is 1, so 2 is not a divisor of 3077)
3077 / 3 = 1025.6666666667 (the remainder is 2, so 3 is not a divisor of 3077)
...
3077 / 54 = 56.981481481481 (the remainder is 53, so 54 is not a divisor of 3077)
3077 / 55 = 55.945454545455 (the remainder is 52, so 55 is not a divisor of 3077)