What are the divisors of 4375?

1, 5, 7, 25, 35, 125, 175, 625, 875, 4375

There is a total of 10 positive divisors.
The sum of these divisors is 6248.
The arithmetic mean is 624.8.

10 odd divisors

1, 5, 7, 25, 35, 125, 175, 625, 875, 4375

How to compute the divisors of 4375?

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 4375 by each of the numbers from 1 to 4375 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)

4375 / 1 = 4375 (the remainder is 0, so 1 is a divisor of 4375)
4375 / 2 = 2187.5 (the remainder is 1, so 2 is not a divisor of 4375)
4375 / 3 = 1458.3333333333 (the remainder is 1, so 3 is not a divisor of 4375)
...
4375 / 4374 = 1.0002286236854 (the remainder is 1, so 4374 is not a divisor of 4375)
4375 / 4375 = 1 (the remainder is 0, so 4375 is a divisor of 4375)

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 4375 (i.e. 66.143782776615). 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 $\frac{N}{d} = D$ )

4375 / 1 = 4375 (the remainder is 0, so 1 and 4375 are divisors of 4375)
4375 / 2 = 2187.5 (the remainder is 1, so 2 is not a divisor of 4375)
4375 / 3 = 1458.3333333333 (the remainder is 1, so 3 is not a divisor of 4375)
...
4375 / 65 = 67.307692307692 (the remainder is 20, so 65 is not a divisor of 4375)
4375 / 66 = 66.287878787879 (the remainder is 19, so 66 is not a divisor of 4375)