What are the divisors of 2547?

1, 3, 9, 283, 849, 2547

There is a total of 6 positive divisors.
The sum of these divisors is 3692.
The arithmetic mean is 615.33333333333.

6 odd divisors

1, 3, 9, 283, 849, 2547

How to compute the divisors of 2547?

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 2547 by each of the numbers from 1 to 2547 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)

2547 / 1 = 2547 (the remainder is 0, so 1 is a divisor of 2547)
2547 / 2 = 1273.5 (the remainder is 1, so 2 is not a divisor of 2547)
2547 / 3 = 849 (the remainder is 0, so 3 is a divisor of 2547)
...
2547 / 2546 = 1.0003927729772 (the remainder is 1, so 2546 is not a divisor of 2547)
2547 / 2547 = 1 (the remainder is 0, so 2547 is a divisor of 2547)

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 2547 (i.e. 50.467811523782). 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 $\frac{N}{d} = D$ )

2547 / 1 = 2547 (the remainder is 0, so 1 and 2547 are divisors of 2547)
2547 / 2 = 1273.5 (the remainder is 1, so 2 is not a divisor of 2547)
2547 / 3 = 849 (the remainder is 0, so 3 and 849 are divisors of 2547)
...
2547 / 49 = 51.979591836735 (the remainder is 48, so 49 is not a divisor of 2547)
2547 / 50 = 50.94 (the remainder is 47, so 50 is not a divisor of 2547)