What are the divisors of 4620?

1, 2, 3, 4, 5, 6, 7, 10, 11, 12, 14, 15, 20, 21, 22, 28, 30, 33, 35, 42, 44, 55, 60, 66, 70, 77, 84, 105, 110, 132, 140, 154, 165, 210, 220, 231, 308, 330, 385, 420, 462, 660, 770, 924, 1155, 1540, 2310, 4620

There is a total of 48 positive divisors.
The sum of these divisors is 16128.
The arithmetic mean is 336.

32 even divisors

2, 4, 6, 10, 12, 14, 20, 22, 28, 30, 42, 44, 60, 66, 70, 84, 110, 132, 140, 154, 210, 220, 308, 330, 420, 462, 660, 770, 924, 1540, 2310, 4620

16 odd divisors

1, 3, 5, 7, 11, 15, 21, 33, 35, 55, 77, 105, 165, 231, 385, 1155

How to compute the divisors of 4620?

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 4620 by each of the numbers from 1 to 4620 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)

4620 / 1 = 4620 (the remainder is 0, so 1 is a divisor of 4620)
4620 / 2 = 2310 (the remainder is 0, so 2 is a divisor of 4620)
4620 / 3 = 1540 (the remainder is 0, so 3 is a divisor of 4620)
...
4620 / 4619 = 1.0002164970773 (the remainder is 1, so 4619 is not a divisor of 4620)
4620 / 4620 = 1 (the remainder is 0, so 4620 is a divisor of 4620)

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 4620 (i.e. 67.970581871866). 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 $\frac{N}{d} = D$ )

4620 / 1 = 4620 (the remainder is 0, so 1 and 4620 are divisors of 4620)
4620 / 2 = 2310 (the remainder is 0, so 2 and 2310 are divisors of 4620)
4620 / 3 = 1540 (the remainder is 0, so 3 and 1540 are divisors of 4620)
...
4620 / 66 = 70 (the remainder is 0, so 66 and 70 are divisors of 4620)
4620 / 67 = 68.955223880597 (the remainder is 64, so 67 is not a divisor of 4620)