What are the divisors of 4245?

1, 3, 5, 15, 283, 849, 1415, 4245

There is a total of 8 positive divisors.
The sum of these divisors is 6816.
The arithmetic mean is 852.

8 odd divisors

1, 3, 5, 15, 283, 849, 1415, 4245

How to compute the divisors of 4245?

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 4245 by each of the numbers from 1 to 4245 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)

4245 / 1 = 4245 (the remainder is 0, so 1 is a divisor of 4245)
4245 / 2 = 2122.5 (the remainder is 1, so 2 is not a divisor of 4245)
4245 / 3 = 1415 (the remainder is 0, so 3 is a divisor of 4245)
...
4245 / 4244 = 1.0002356267672 (the remainder is 1, so 4244 is not a divisor of 4245)
4245 / 4245 = 1 (the remainder is 0, so 4245 is a divisor of 4245)

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 4245 (i.e. 65.153664517048). 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 $\frac{N}{d} = D$ )

4245 / 1 = 4245 (the remainder is 0, so 1 and 4245 are divisors of 4245)
4245 / 2 = 2122.5 (the remainder is 1, so 2 is not a divisor of 4245)
4245 / 3 = 1415 (the remainder is 0, so 3 and 1415 are divisors of 4245)
...
4245 / 64 = 66.328125 (the remainder is 21, so 64 is not a divisor of 4245)
4245 / 65 = 65.307692307692 (the remainder is 20, so 65 is not a divisor of 4245)