What are the divisors of 4765?

1, 5, 953, 4765

There is a total of 4 positive divisors.
The sum of these divisors is 5724.
The arithmetic mean is 1431.

4 odd divisors

1, 5, 953, 4765

How to compute the divisors of 4765?

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 4765 by each of the numbers from 1 to 4765 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)

4765 / 1 = 4765 (the remainder is 0, so 1 is a divisor of 4765)
4765 / 2 = 2382.5 (the remainder is 1, so 2 is not a divisor of 4765)
4765 / 3 = 1588.3333333333 (the remainder is 1, so 3 is not a divisor of 4765)
...
4765 / 4764 = 1.0002099076406 (the remainder is 1, so 4764 is not a divisor of 4765)
4765 / 4765 = 1 (the remainder is 0, so 4765 is a divisor of 4765)

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 4765 (i.e. 69.028979421689). 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 $\frac{N}{d} = D$ )

4765 / 1 = 4765 (the remainder is 0, so 1 and 4765 are divisors of 4765)
4765 / 2 = 2382.5 (the remainder is 1, so 2 is not a divisor of 4765)
4765 / 3 = 1588.3333333333 (the remainder is 1, so 3 is not a divisor of 4765)
...
4765 / 68 = 70.073529411765 (the remainder is 5, so 68 is not a divisor of 4765)
4765 / 69 = 69.057971014493 (the remainder is 4, so 69 is not a divisor of 4765)