What are the divisors of 4770?

1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 53, 90, 106, 159, 265, 318, 477, 530, 795, 954, 1590, 2385, 4770

There is a total of 24 positive divisors.
The sum of these divisors is 12636.
The arithmetic mean is 526.5.

12 even divisors

2, 6, 10, 18, 30, 90, 106, 318, 530, 954, 1590, 4770

12 odd divisors

1, 3, 5, 9, 15, 45, 53, 159, 265, 477, 795, 2385

How to compute the divisors of 4770?

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 4770 by each of the numbers from 1 to 4770 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)

4770 / 1 = 4770 (the remainder is 0, so 1 is a divisor of 4770)
4770 / 2 = 2385 (the remainder is 0, so 2 is a divisor of 4770)
4770 / 3 = 1590 (the remainder is 0, so 3 is a divisor of 4770)
...
4770 / 4769 = 1.0002096875655 (the remainder is 1, so 4769 is not a divisor of 4770)
4770 / 4770 = 1 (the remainder is 0, so 4770 is a divisor of 4770)

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 4770 (i.e. 69.065186599328). 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 $\frac{N}{d} = D$ )

4770 / 1 = 4770 (the remainder is 0, so 1 and 4770 are divisors of 4770)
4770 / 2 = 2385 (the remainder is 0, so 2 and 2385 are divisors of 4770)
4770 / 3 = 1590 (the remainder is 0, so 3 and 1590 are divisors of 4770)
...
4770 / 68 = 70.147058823529 (the remainder is 10, so 68 is not a divisor of 4770)
4770 / 69 = 69.130434782609 (the remainder is 9, so 69 is not a divisor of 4770)