What are the divisors of 2753?

1, 2753

There is a total of 2 positive divisors.
The sum of these divisors is 2754.
The arithmetic mean is 1377.

2 odd divisors

1, 2753

How to compute the divisors of 2753?

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 2753 by each of the numbers from 1 to 2753 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)

2753 / 1 = 2753 (the remainder is 0, so 1 is a divisor of 2753)
2753 / 2 = 1376.5 (the remainder is 1, so 2 is not a divisor of 2753)
2753 / 3 = 917.66666666667 (the remainder is 2, so 3 is not a divisor of 2753)
...
2753 / 2752 = 1.000363372093 (the remainder is 1, so 2752 is not a divisor of 2753)
2753 / 2753 = 1 (the remainder is 0, so 2753 is a divisor of 2753)

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 2753 (i.e. 52.46903848938). 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 $\frac{N}{d} = D$ )

2753 / 1 = 2753 (the remainder is 0, so 1 and 2753 are divisors of 2753)
2753 / 2 = 1376.5 (the remainder is 1, so 2 is not a divisor of 2753)
2753 / 3 = 917.66666666667 (the remainder is 2, so 3 is not a divisor of 2753)
...
2753 / 51 = 53.980392156863 (the remainder is 50, so 51 is not a divisor of 2753)
2753 / 52 = 52.942307692308 (the remainder is 49, so 52 is not a divisor of 2753)