What are the divisors of 3063?

1, 3, 1021, 3063

There is a total of 4 positive divisors.
The sum of these divisors is 4088.
The arithmetic mean is 1022.

4 odd divisors

1, 3, 1021, 3063

How to compute the divisors of 3063?

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 3063 by each of the numbers from 1 to 3063 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)

3063 / 1 = 3063 (the remainder is 0, so 1 is a divisor of 3063)
3063 / 2 = 1531.5 (the remainder is 1, so 2 is not a divisor of 3063)
3063 / 3 = 1021 (the remainder is 0, so 3 is a divisor of 3063)
...
3063 / 3062 = 1.0003265839321 (the remainder is 1, so 3062 is not a divisor of 3063)
3063 / 3063 = 1 (the remainder is 0, so 3063 is a divisor of 3063)

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 3063 (i.e. 55.344376408087). 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 $\frac{N}{d} = D$ )

3063 / 1 = 3063 (the remainder is 0, so 1 and 3063 are divisors of 3063)
3063 / 2 = 1531.5 (the remainder is 1, so 2 is not a divisor of 3063)
3063 / 3 = 1021 (the remainder is 0, so 3 and 1021 are divisors of 3063)
...
3063 / 54 = 56.722222222222 (the remainder is 39, so 54 is not a divisor of 3063)
3063 / 55 = 55.690909090909 (the remainder is 38, so 55 is not a divisor of 3063)