What are the divisors of 4890?

1, 2, 3, 5, 6, 10, 15, 30, 163, 326, 489, 815, 978, 1630, 2445, 4890

There is a total of 16 positive divisors.
The sum of these divisors is 11808.
The arithmetic mean is 738.

8 even divisors

2, 6, 10, 30, 326, 978, 1630, 4890

8 odd divisors

1, 3, 5, 15, 163, 489, 815, 2445

How to compute the divisors of 4890?

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 4890 by each of the numbers from 1 to 4890 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)

4890 / 1 = 4890 (the remainder is 0, so 1 is a divisor of 4890)
4890 / 2 = 2445 (the remainder is 0, so 2 is a divisor of 4890)
4890 / 3 = 1630 (the remainder is 0, so 3 is a divisor of 4890)
...
4890 / 4889 = 1.0002045408059 (the remainder is 1, so 4889 is not a divisor of 4890)
4890 / 4890 = 1 (the remainder is 0, so 4890 is a divisor of 4890)

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 4890 (i.e. 69.928534948188). 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 $\frac{N}{d} = D$ )

4890 / 1 = 4890 (the remainder is 0, so 1 and 4890 are divisors of 4890)
4890 / 2 = 2445 (the remainder is 0, so 2 and 2445 are divisors of 4890)
4890 / 3 = 1630 (the remainder is 0, so 3 and 1630 are divisors of 4890)
...
4890 / 68 = 71.911764705882 (the remainder is 62, so 68 is not a divisor of 4890)
4890 / 69 = 70.869565217391 (the remainder is 60, so 69 is not a divisor of 4890)