What are the divisors of 2735?

1, 5, 547, 2735

There is a total of 4 positive divisors.
The sum of these divisors is 3288.
The arithmetic mean is 822.

4 odd divisors

1, 5, 547, 2735

How to compute the divisors of 2735?

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 2735 by each of the numbers from 1 to 2735 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)

2735 / 1 = 2735 (the remainder is 0, so 1 is a divisor of 2735)
2735 / 2 = 1367.5 (the remainder is 1, so 2 is not a divisor of 2735)
2735 / 3 = 911.66666666667 (the remainder is 2, so 3 is not a divisor of 2735)
...
2735 / 2734 = 1.0003657644477 (the remainder is 1, so 2734 is not a divisor of 2735)
2735 / 2735 = 1 (the remainder is 0, so 2735 is a divisor of 2735)

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 2735 (i.e. 52.297227459972). 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 $\frac{N}{d} = D$ )

2735 / 1 = 2735 (the remainder is 0, so 1 and 2735 are divisors of 2735)
2735 / 2 = 1367.5 (the remainder is 1, so 2 is not a divisor of 2735)
2735 / 3 = 911.66666666667 (the remainder is 2, so 3 is not a divisor of 2735)
...
2735 / 51 = 53.627450980392 (the remainder is 32, so 51 is not a divisor of 2735)
2735 / 52 = 52.596153846154 (the remainder is 31, so 52 is not a divisor of 2735)