What are the divisors of 4755?

1, 3, 5, 15, 317, 951, 1585, 4755

There is a total of 8 positive divisors.
The sum of these divisors is 7632.
The arithmetic mean is 954.

8 odd divisors

1, 3, 5, 15, 317, 951, 1585, 4755

How to compute the divisors of 4755?

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 4755 by each of the numbers from 1 to 4755 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)

4755 / 1 = 4755 (the remainder is 0, so 1 is a divisor of 4755)
4755 / 2 = 2377.5 (the remainder is 1, so 2 is not a divisor of 4755)
4755 / 3 = 1585 (the remainder is 0, so 3 is a divisor of 4755)
...
4755 / 4754 = 1.0002103491796 (the remainder is 1, so 4754 is not a divisor of 4755)
4755 / 4755 = 1 (the remainder is 0, so 4755 is a divisor of 4755)

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 4755 (i.e. 68.956508032237). 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 $\frac{N}{d} = D$ )

4755 / 1 = 4755 (the remainder is 0, so 1 and 4755 are divisors of 4755)
4755 / 2 = 2377.5 (the remainder is 1, so 2 is not a divisor of 4755)
4755 / 3 = 1585 (the remainder is 0, so 3 and 1585 are divisors of 4755)
...
4755 / 67 = 70.970149253731 (the remainder is 65, so 67 is not a divisor of 4755)
4755 / 68 = 69.926470588235 (the remainder is 63, so 68 is not a divisor of 4755)