What are the divisors of 2754?

1, 2, 3, 6, 9, 17, 18, 27, 34, 51, 54, 81, 102, 153, 162, 306, 459, 918, 1377, 2754

There is a total of 20 positive divisors.
The sum of these divisors is 6534.
The arithmetic mean is 326.7.

10 even divisors

2, 6, 18, 34, 54, 102, 162, 306, 918, 2754

10 odd divisors

1, 3, 9, 17, 27, 51, 81, 153, 459, 1377

How to compute the divisors of 2754?

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 2754 by each of the numbers from 1 to 2754 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)

2754 / 1 = 2754 (the remainder is 0, so 1 is a divisor of 2754)
2754 / 2 = 1377 (the remainder is 0, so 2 is a divisor of 2754)
2754 / 3 = 918 (the remainder is 0, so 3 is a divisor of 2754)
...
2754 / 2753 = 1.0003632401017 (the remainder is 1, so 2753 is not a divisor of 2754)
2754 / 2754 = 1 (the remainder is 0, so 2754 is a divisor of 2754)

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 2754 (i.e. 52.478567053608). 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 $\frac{N}{d} = D$ )

2754 / 1 = 2754 (the remainder is 0, so 1 and 2754 are divisors of 2754)
2754 / 2 = 1377 (the remainder is 0, so 2 and 1377 are divisors of 2754)
2754 / 3 = 918 (the remainder is 0, so 3 and 918 are divisors of 2754)
...
2754 / 51 = 54 (the remainder is 0, so 51 and 54 are divisors of 2754)
2754 / 52 = 52.961538461538 (the remainder is 50, so 52 is not a divisor of 2754)