What are the divisors of 4764?

1, 2, 3, 4, 6, 12, 397, 794, 1191, 1588, 2382, 4764

There is a total of 12 positive divisors.
The sum of these divisors is 11144.
The arithmetic mean is 928.66666666667.

8 even divisors

2, 4, 6, 12, 794, 1588, 2382, 4764

4 odd divisors

1, 3, 397, 1191

How to compute the divisors of 4764?

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 4764 by each of the numbers from 1 to 4764 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)

4764 / 1 = 4764 (the remainder is 0, so 1 is a divisor of 4764)
4764 / 2 = 2382 (the remainder is 0, so 2 is a divisor of 4764)
4764 / 3 = 1588 (the remainder is 0, so 3 is a divisor of 4764)
...
4764 / 4763 = 1.0002099517111 (the remainder is 1, so 4763 is not a divisor of 4764)
4764 / 4764 = 1 (the remainder is 0, so 4764 is a divisor of 4764)

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 4764 (i.e. 69.02173570695). 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 $\frac{N}{d} = D$ )

4764 / 1 = 4764 (the remainder is 0, so 1 and 4764 are divisors of 4764)
4764 / 2 = 2382 (the remainder is 0, so 2 and 2382 are divisors of 4764)
4764 / 3 = 1588 (the remainder is 0, so 3 and 1588 are divisors of 4764)
...
4764 / 68 = 70.058823529412 (the remainder is 4, so 68 is not a divisor of 4764)
4764 / 69 = 69.04347826087 (the remainder is 3, so 69 is not a divisor of 4764)