What are the divisors of 3076?

1, 2, 4, 769, 1538, 3076

There is a total of 6 positive divisors.
The sum of these divisors is 5390.
The arithmetic mean is 898.33333333333.

4 even divisors

2, 4, 1538, 3076

2 odd divisors

1, 769

How to compute the divisors of 3076?

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 3076 by each of the numbers from 1 to 3076 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)

3076 / 1 = 3076 (the remainder is 0, so 1 is a divisor of 3076)
3076 / 2 = 1538 (the remainder is 0, so 2 is a divisor of 3076)
3076 / 3 = 1025.3333333333 (the remainder is 1, so 3 is not a divisor of 3076)
...
3076 / 3075 = 1.000325203252 (the remainder is 1, so 3075 is not a divisor of 3076)
3076 / 3076 = 1 (the remainder is 0, so 3076 is a divisor of 3076)

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 3076 (i.e. 55.461698495448). 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 $\frac{N}{d} = D$ )

3076 / 1 = 3076 (the remainder is 0, so 1 and 3076 are divisors of 3076)
3076 / 2 = 1538 (the remainder is 0, so 2 and 1538 are divisors of 3076)
3076 / 3 = 1025.3333333333 (the remainder is 1, so 3 is not a divisor of 3076)
...
3076 / 54 = 56.962962962963 (the remainder is 52, so 54 is not a divisor of 3076)
3076 / 55 = 55.927272727273 (the remainder is 51, so 55 is not a divisor of 3076)