What are the divisors of 5375?

1, 5, 25, 43, 125, 215, 1075, 5375

There is a total of 8 positive divisors.
The sum of these divisors is 6864.
The arithmetic mean is 858.

8 odd divisors

1, 5, 25, 43, 125, 215, 1075, 5375

How to compute the divisors of 5375?

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 5375 by each of the numbers from 1 to 5375 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)

5375 / 1 = 5375 (the remainder is 0, so 1 is a divisor of 5375)
5375 / 2 = 2687.5 (the remainder is 1, so 2 is not a divisor of 5375)
5375 / 3 = 1791.6666666667 (the remainder is 2, so 3 is not a divisor of 5375)
...
5375 / 5374 = 1.0001860811314 (the remainder is 1, so 5374 is not a divisor of 5375)
5375 / 5375 = 1 (the remainder is 0, so 5375 is a divisor of 5375)

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 5375 (i.e. 73.314391493076). 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 $\frac{N}{d} = D$ )

5375 / 1 = 5375 (the remainder is 0, so 1 and 5375 are divisors of 5375)
5375 / 2 = 2687.5 (the remainder is 1, so 2 is not a divisor of 5375)
5375 / 3 = 1791.6666666667 (the remainder is 2, so 3 is not a divisor of 5375)
...
5375 / 72 = 74.652777777778 (the remainder is 47, so 72 is not a divisor of 5375)
5375 / 73 = 73.630136986301 (the remainder is 46, so 73 is not a divisor of 5375)