What are the divisors of 4325?

1, 5, 25, 173, 865, 4325

There is a total of 6 positive divisors.
The sum of these divisors is 5394.
The arithmetic mean is 899.

6 odd divisors

1, 5, 25, 173, 865, 4325

How to compute the divisors of 4325?

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 4325 by each of the numbers from 1 to 4325 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)

4325 / 1 = 4325 (the remainder is 0, so 1 is a divisor of 4325)
4325 / 2 = 2162.5 (the remainder is 1, so 2 is not a divisor of 4325)
4325 / 3 = 1441.6666666667 (the remainder is 2, so 3 is not a divisor of 4325)
...
4325 / 4324 = 1.0002312673451 (the remainder is 1, so 4324 is not a divisor of 4325)
4325 / 4325 = 1 (the remainder is 0, so 4325 is a divisor of 4325)

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 4325 (i.e. 65.76473218983). 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 $\frac{N}{d} = D$ )

4325 / 1 = 4325 (the remainder is 0, so 1 and 4325 are divisors of 4325)
4325 / 2 = 2162.5 (the remainder is 1, so 2 is not a divisor of 4325)
4325 / 3 = 1441.6666666667 (the remainder is 2, so 3 is not a divisor of 4325)
...
4325 / 64 = 67.578125 (the remainder is 37, so 64 is not a divisor of 4325)
4325 / 65 = 66.538461538462 (the remainder is 35, so 65 is not a divisor of 4325)