What are the divisors of 4685?

1, 5, 937, 4685

There is a total of 4 positive divisors.
The sum of these divisors is 5628.
The arithmetic mean is 1407.

4 odd divisors

1, 5, 937, 4685

How to compute the divisors of 4685?

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 4685 by each of the numbers from 1 to 4685 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)

4685 / 1 = 4685 (the remainder is 0, so 1 is a divisor of 4685)
4685 / 2 = 2342.5 (the remainder is 1, so 2 is not a divisor of 4685)
4685 / 3 = 1561.6666666667 (the remainder is 2, so 3 is not a divisor of 4685)
...
4685 / 4684 = 1.0002134927412 (the remainder is 1, so 4684 is not a divisor of 4685)
4685 / 4685 = 1 (the remainder is 0, so 4685 is a divisor of 4685)

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 4685 (i.e. 68.44705983459). 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 $\frac{N}{d} = D$ )

4685 / 1 = 4685 (the remainder is 0, so 1 and 4685 are divisors of 4685)
4685 / 2 = 2342.5 (the remainder is 1, so 2 is not a divisor of 4685)
4685 / 3 = 1561.6666666667 (the remainder is 2, so 3 is not a divisor of 4685)
...
4685 / 67 = 69.925373134328 (the remainder is 62, so 67 is not a divisor of 4685)
4685 / 68 = 68.897058823529 (the remainder is 61, so 68 is not a divisor of 4685)