What are the divisors of 5975?

1, 5, 25, 239, 1195, 5975

There is a total of 6 positive divisors.
The sum of these divisors is 7440.
The arithmetic mean is 1240.

6 odd divisors

1, 5, 25, 239, 1195, 5975

How to compute the divisors of 5975?

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 5975 by each of the numbers from 1 to 5975 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)

5975 / 1 = 5975 (the remainder is 0, so 1 is a divisor of 5975)
5975 / 2 = 2987.5 (the remainder is 1, so 2 is not a divisor of 5975)
5975 / 3 = 1991.6666666667 (the remainder is 2, so 3 is not a divisor of 5975)
...
5975 / 5974 = 1.0001673920321 (the remainder is 1, so 5974 is not a divisor of 5975)
5975 / 5975 = 1 (the remainder is 0, so 5975 is a divisor of 5975)

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 5975 (i.e. 77.298124168702). 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 $\frac{N}{d} = D$ )

5975 / 1 = 5975 (the remainder is 0, so 1 and 5975 are divisors of 5975)
5975 / 2 = 2987.5 (the remainder is 1, so 2 is not a divisor of 5975)
5975 / 3 = 1991.6666666667 (the remainder is 2, so 3 is not a divisor of 5975)
...
5975 / 76 = 78.618421052632 (the remainder is 47, so 76 is not a divisor of 5975)
5975 / 77 = 77.597402597403 (the remainder is 46, so 77 is not a divisor of 5975)