What are the divisors of 2733?

1, 3, 911, 2733

There is a total of 4 positive divisors.
The sum of these divisors is 3648.
The arithmetic mean is 912.

4 odd divisors

1, 3, 911, 2733

How to compute the divisors of 2733?

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 2733 by each of the numbers from 1 to 2733 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)

2733 / 1 = 2733 (the remainder is 0, so 1 is a divisor of 2733)
2733 / 2 = 1366.5 (the remainder is 1, so 2 is not a divisor of 2733)
2733 / 3 = 911 (the remainder is 0, so 3 is a divisor of 2733)
...
2733 / 2732 = 1.0003660322108 (the remainder is 1, so 2732 is not a divisor of 2733)
2733 / 2733 = 1 (the remainder is 0, so 2733 is a divisor of 2733)

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 2733 (i.e. 52.278102490431). 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 $\frac{N}{d} = D$ )

2733 / 1 = 2733 (the remainder is 0, so 1 and 2733 are divisors of 2733)
2733 / 2 = 1366.5 (the remainder is 1, so 2 is not a divisor of 2733)
2733 / 3 = 911 (the remainder is 0, so 3 and 911 are divisors of 2733)
...
2733 / 51 = 53.588235294118 (the remainder is 30, so 51 is not a divisor of 2733)
2733 / 52 = 52.557692307692 (the remainder is 29, so 52 is not a divisor of 2733)