What are the divisors of 4782?

1, 2, 3, 6, 797, 1594, 2391, 4782

There is a total of 8 positive divisors.
The sum of these divisors is 9576.
The arithmetic mean is 1197.

4 even divisors

2, 6, 1594, 4782

4 odd divisors

1, 3, 797, 2391

How to compute the divisors of 4782?

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 4782 by each of the numbers from 1 to 4782 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)

4782 / 1 = 4782 (the remainder is 0, so 1 is a divisor of 4782)
4782 / 2 = 2391 (the remainder is 0, so 2 is a divisor of 4782)
4782 / 3 = 1594 (the remainder is 0, so 3 is a divisor of 4782)
...
4782 / 4781 = 1.0002091612633 (the remainder is 1, so 4781 is not a divisor of 4782)
4782 / 4782 = 1 (the remainder is 0, so 4782 is a divisor of 4782)

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 4782 (i.e. 69.152006478482). 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 $\frac{N}{d} = D$ )

4782 / 1 = 4782 (the remainder is 0, so 1 and 4782 are divisors of 4782)
4782 / 2 = 2391 (the remainder is 0, so 2 and 2391 are divisors of 4782)
4782 / 3 = 1594 (the remainder is 0, so 3 and 1594 are divisors of 4782)
...
4782 / 68 = 70.323529411765 (the remainder is 22, so 68 is not a divisor of 4782)
4782 / 69 = 69.304347826087 (the remainder is 21, so 69 is not a divisor of 4782)