What are the divisors of 3064?

1, 2, 4, 8, 383, 766, 1532, 3064

There is a total of 8 positive divisors.
The sum of these divisors is 5760.
The arithmetic mean is 720.

6 even divisors

2, 4, 8, 766, 1532, 3064

2 odd divisors

1, 383

How to compute the divisors of 3064?

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 3064 by each of the numbers from 1 to 3064 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)

3064 / 1 = 3064 (the remainder is 0, so 1 is a divisor of 3064)
3064 / 2 = 1532 (the remainder is 0, so 2 is a divisor of 3064)
3064 / 3 = 1021.3333333333 (the remainder is 1, so 3 is not a divisor of 3064)
...
3064 / 3063 = 1.0003264773098 (the remainder is 1, so 3063 is not a divisor of 3064)
3064 / 3064 = 1 (the remainder is 0, so 3064 is a divisor of 3064)

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 3064 (i.e. 55.353410012392). 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 $\frac{N}{d} = D$ )

3064 / 1 = 3064 (the remainder is 0, so 1 and 3064 are divisors of 3064)
3064 / 2 = 1532 (the remainder is 0, so 2 and 1532 are divisors of 3064)
3064 / 3 = 1021.3333333333 (the remainder is 1, so 3 is not a divisor of 3064)
...
3064 / 54 = 56.740740740741 (the remainder is 40, so 54 is not a divisor of 3064)
3064 / 55 = 55.709090909091 (the remainder is 39, so 55 is not a divisor of 3064)