What are the divisors of 2055?

1, 3, 5, 15, 137, 411, 685, 2055

There is a total of 8 positive divisors.
The sum of these divisors is 3312.
The arithmetic mean is 414.

8 odd divisors

1, 3, 5, 15, 137, 411, 685, 2055

How to compute the divisors of 2055?

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 2055 by each of the numbers from 1 to 2055 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)

2055 / 1 = 2055 (the remainder is 0, so 1 is a divisor of 2055)
2055 / 2 = 1027.5 (the remainder is 1, so 2 is not a divisor of 2055)
2055 / 3 = 685 (the remainder is 0, so 3 is a divisor of 2055)
...
2055 / 2054 = 1.0004868549172 (the remainder is 1, so 2054 is not a divisor of 2055)
2055 / 2055 = 1 (the remainder is 0, so 2055 is a divisor of 2055)

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 2055 (i.e. 45.332107826573). 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 $\frac{N}{d} = D$ )

2055 / 1 = 2055 (the remainder is 0, so 1 and 2055 are divisors of 2055)
2055 / 2 = 1027.5 (the remainder is 1, so 2 is not a divisor of 2055)
2055 / 3 = 685 (the remainder is 0, so 3 and 685 are divisors of 2055)
...
2055 / 44 = 46.704545454545 (the remainder is 31, so 44 is not a divisor of 2055)
2055 / 45 = 45.666666666667 (the remainder is 30, so 45 is not a divisor of 2055)