What are the divisors of 4875?

1, 3, 5, 13, 15, 25, 39, 65, 75, 125, 195, 325, 375, 975, 1625, 4875

There is a total of 16 positive divisors.
The sum of these divisors is 8736.
The arithmetic mean is 546.

16 odd divisors

1, 3, 5, 13, 15, 25, 39, 65, 75, 125, 195, 325, 375, 975, 1625, 4875

How to compute the divisors of 4875?

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 4875 by each of the numbers from 1 to 4875 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)

4875 / 1 = 4875 (the remainder is 0, so 1 is a divisor of 4875)
4875 / 2 = 2437.5 (the remainder is 1, so 2 is not a divisor of 4875)
4875 / 3 = 1625 (the remainder is 0, so 3 is a divisor of 4875)
...
4875 / 4874 = 1.0002051702913 (the remainder is 1, so 4874 is not a divisor of 4875)
4875 / 4875 = 1 (the remainder is 0, so 4875 is a divisor of 4875)

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 4875 (i.e. 69.821200218845). 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 $\frac{N}{d} = D$ )

4875 / 1 = 4875 (the remainder is 0, so 1 and 4875 are divisors of 4875)
4875 / 2 = 2437.5 (the remainder is 1, so 2 is not a divisor of 4875)
4875 / 3 = 1625 (the remainder is 0, so 3 and 1625 are divisors of 4875)
...
4875 / 68 = 71.691176470588 (the remainder is 47, so 68 is not a divisor of 4875)
4875 / 69 = 70.652173913043 (the remainder is 45, so 69 is not a divisor of 4875)