What are the divisors of 5953?

1, 5953

There is a total of 2 positive divisors.
The sum of these divisors is 5954.
The arithmetic mean is 2977.

2 odd divisors

1, 5953

How to compute the divisors of 5953?

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 5953 by each of the numbers from 1 to 5953 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)

5953 / 1 = 5953 (the remainder is 0, so 1 is a divisor of 5953)
5953 / 2 = 2976.5 (the remainder is 1, so 2 is not a divisor of 5953)
5953 / 3 = 1984.3333333333 (the remainder is 1, so 3 is not a divisor of 5953)
...
5953 / 5952 = 1.0001680107527 (the remainder is 1, so 5952 is not a divisor of 5953)
5953 / 5953 = 1 (the remainder is 0, so 5953 is a divisor of 5953)

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 5953 (i.e. 77.155686763841). 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 $\frac{N}{d} = D$ )

5953 / 1 = 5953 (the remainder is 0, so 1 and 5953 are divisors of 5953)
5953 / 2 = 2976.5 (the remainder is 1, so 2 is not a divisor of 5953)
5953 / 3 = 1984.3333333333 (the remainder is 1, so 3 is not a divisor of 5953)
...
5953 / 76 = 78.328947368421 (the remainder is 25, so 76 is not a divisor of 5953)
5953 / 77 = 77.311688311688 (the remainder is 24, so 77 is not a divisor of 5953)