What are the divisors of 5853?

1, 3, 1951, 5853

There is a total of 4 positive divisors.
The sum of these divisors is 7808.
The arithmetic mean is 1952.

4 odd divisors

1, 3, 1951, 5853

How to compute the divisors of 5853?

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 5853 by each of the numbers from 1 to 5853 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)

5853 / 1 = 5853 (the remainder is 0, so 1 is a divisor of 5853)
5853 / 2 = 2926.5 (the remainder is 1, so 2 is not a divisor of 5853)
5853 / 3 = 1951 (the remainder is 0, so 3 is a divisor of 5853)
...
5853 / 5852 = 1.0001708817498 (the remainder is 1, so 5852 is not a divisor of 5853)
5853 / 5853 = 1 (the remainder is 0, so 5853 is a divisor of 5853)

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 5853 (i.e. 76.504901803741). 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 $\frac{N}{d} = D$ )

5853 / 1 = 5853 (the remainder is 0, so 1 and 5853 are divisors of 5853)
5853 / 2 = 2926.5 (the remainder is 1, so 2 is not a divisor of 5853)
5853 / 3 = 1951 (the remainder is 0, so 3 and 1951 are divisors of 5853)
...
5853 / 75 = 78.04 (the remainder is 3, so 75 is not a divisor of 5853)
5853 / 76 = 77.013157894737 (the remainder is 1, so 76 is not a divisor of 5853)