What are the divisors of 4860?

1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 27, 30, 36, 45, 54, 60, 81, 90, 108, 135, 162, 180, 243, 270, 324, 405, 486, 540, 810, 972, 1215, 1620, 2430, 4860

There is a total of 36 positive divisors.
The sum of these divisors is 15288.
The arithmetic mean is 424.66666666667.

24 even divisors

2, 4, 6, 10, 12, 18, 20, 30, 36, 54, 60, 90, 108, 162, 180, 270, 324, 486, 540, 810, 972, 1620, 2430, 4860

12 odd divisors

1, 3, 5, 9, 15, 27, 45, 81, 135, 243, 405, 1215

How to compute the divisors of 4860?

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 4860 by each of the numbers from 1 to 4860 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)

4860 / 1 = 4860 (the remainder is 0, so 1 is a divisor of 4860)
4860 / 2 = 2430 (the remainder is 0, so 2 is a divisor of 4860)
4860 / 3 = 1620 (the remainder is 0, so 3 is a divisor of 4860)
...
4860 / 4859 = 1.0002058036633 (the remainder is 1, so 4859 is not a divisor of 4860)
4860 / 4860 = 1 (the remainder is 0, so 4860 is a divisor of 4860)

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 4860 (i.e. 69.713700231733). 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 $\frac{N}{d} = D$ )

4860 / 1 = 4860 (the remainder is 0, so 1 and 4860 are divisors of 4860)
4860 / 2 = 2430 (the remainder is 0, so 2 and 2430 are divisors of 4860)
4860 / 3 = 1620 (the remainder is 0, so 3 and 1620 are divisors of 4860)
...
4860 / 68 = 71.470588235294 (the remainder is 32, so 68 is not a divisor of 4860)
4860 / 69 = 70.434782608696 (the remainder is 30, so 69 is not a divisor of 4860)