What are the divisors of 4754?

1, 2, 2377, 4754

There is a total of 4 positive divisors.
The sum of these divisors is 7134.
The arithmetic mean is 1783.5.

2 even divisors

2, 4754

2 odd divisors

1, 2377

How to compute the divisors of 4754?

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 4754 by each of the numbers from 1 to 4754 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)

4754 / 1 = 4754 (the remainder is 0, so 1 is a divisor of 4754)
4754 / 2 = 2377 (the remainder is 0, so 2 is a divisor of 4754)
4754 / 3 = 1584.6666666667 (the remainder is 2, so 3 is not a divisor of 4754)
...
4754 / 4753 = 1.0002103934357 (the remainder is 1, so 4753 is not a divisor of 4754)
4754 / 4754 = 1 (the remainder is 0, so 4754 is a divisor of 4754)

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 4754 (i.e. 68.949256703753). 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 $\frac{N}{d} = D$ )

4754 / 1 = 4754 (the remainder is 0, so 1 and 4754 are divisors of 4754)
4754 / 2 = 2377 (the remainder is 0, so 2 and 2377 are divisors of 4754)
4754 / 3 = 1584.6666666667 (the remainder is 2, so 3 is not a divisor of 4754)
...
4754 / 67 = 70.955223880597 (the remainder is 64, so 67 is not a divisor of 4754)
4754 / 68 = 69.911764705882 (the remainder is 62, so 68 is not a divisor of 4754)