What are the divisors of 4425?

1, 3, 5, 15, 25, 59, 75, 177, 295, 885, 1475, 4425

There is a total of 12 positive divisors.
The sum of these divisors is 7440.
The arithmetic mean is 620.

12 odd divisors

1, 3, 5, 15, 25, 59, 75, 177, 295, 885, 1475, 4425

How to compute the divisors of 4425?

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 4425 by each of the numbers from 1 to 4425 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)

4425 / 1 = 4425 (the remainder is 0, so 1 is a divisor of 4425)
4425 / 2 = 2212.5 (the remainder is 1, so 2 is not a divisor of 4425)
4425 / 3 = 1475 (the remainder is 0, so 3 is a divisor of 4425)
...
4425 / 4424 = 1.000226039783 (the remainder is 1, so 4424 is not a divisor of 4425)
4425 / 4425 = 1 (the remainder is 0, so 4425 is a divisor of 4425)

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 4425 (i.e. 66.52067347825). 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 $\frac{N}{d} = D$ )

4425 / 1 = 4425 (the remainder is 0, so 1 and 4425 are divisors of 4425)
4425 / 2 = 2212.5 (the remainder is 1, so 2 is not a divisor of 4425)
4425 / 3 = 1475 (the remainder is 0, so 3 and 1475 are divisors of 4425)
...
4425 / 65 = 68.076923076923 (the remainder is 5, so 65 is not a divisor of 4425)
4425 / 66 = 67.045454545455 (the remainder is 3, so 66 is not a divisor of 4425)