What are the divisors of 4695?

1, 3, 5, 15, 313, 939, 1565, 4695

There is a total of 8 positive divisors.
The sum of these divisors is 7536.
The arithmetic mean is 942.

8 odd divisors

1, 3, 5, 15, 313, 939, 1565, 4695

How to compute the divisors of 4695?

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 4695 by each of the numbers from 1 to 4695 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)

4695 / 1 = 4695 (the remainder is 0, so 1 is a divisor of 4695)
4695 / 2 = 2347.5 (the remainder is 1, so 2 is not a divisor of 4695)
4695 / 3 = 1565 (the remainder is 0, so 3 is a divisor of 4695)
...
4695 / 4694 = 1.0002130379207 (the remainder is 1, so 4694 is not a divisor of 4695)
4695 / 4695 = 1 (the remainder is 0, so 4695 is a divisor of 4695)

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 4695 (i.e. 68.520070052504). 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 $\frac{N}{d} = D$ )

4695 / 1 = 4695 (the remainder is 0, so 1 and 4695 are divisors of 4695)
4695 / 2 = 2347.5 (the remainder is 1, so 2 is not a divisor of 4695)
4695 / 3 = 1565 (the remainder is 0, so 3 and 1565 are divisors of 4695)
...
4695 / 67 = 70.074626865672 (the remainder is 5, so 67 is not a divisor of 4695)
4695 / 68 = 69.044117647059 (the remainder is 3, so 68 is not a divisor of 4695)