What are the divisors of 2757?

1, 3, 919, 2757

There is a total of 4 positive divisors.
The sum of these divisors is 3680.
The arithmetic mean is 920.

4 odd divisors

1, 3, 919, 2757

How to compute the divisors of 2757?

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 2757 by each of the numbers from 1 to 2757 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)

2757 / 1 = 2757 (the remainder is 0, so 1 is a divisor of 2757)
2757 / 2 = 1378.5 (the remainder is 1, so 2 is not a divisor of 2757)
2757 / 3 = 919 (the remainder is 0, so 3 is a divisor of 2757)
...
2757 / 2756 = 1.0003628447025 (the remainder is 1, so 2756 is not a divisor of 2757)
2757 / 2757 = 1 (the remainder is 0, so 2757 is a divisor of 2757)

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 2757 (i.e. 52.5071423713). 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 $\frac{N}{d} = D$ )

2757 / 1 = 2757 (the remainder is 0, so 1 and 2757 are divisors of 2757)
2757 / 2 = 1378.5 (the remainder is 1, so 2 is not a divisor of 2757)
2757 / 3 = 919 (the remainder is 0, so 3 and 919 are divisors of 2757)
...
2757 / 51 = 54.058823529412 (the remainder is 3, so 51 is not a divisor of 2757)
2757 / 52 = 53.019230769231 (the remainder is 1, so 52 is not a divisor of 2757)