What are the divisors of 4980?

1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60, 83, 166, 249, 332, 415, 498, 830, 996, 1245, 1660, 2490, 4980

There is a total of 24 positive divisors.
The sum of these divisors is 14112.
The arithmetic mean is 588.

16 even divisors

2, 4, 6, 10, 12, 20, 30, 60, 166, 332, 498, 830, 996, 1660, 2490, 4980

8 odd divisors

1, 3, 5, 15, 83, 249, 415, 1245

How to compute the divisors of 4980?

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 4980 by each of the numbers from 1 to 4980 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)

4980 / 1 = 4980 (the remainder is 0, so 1 is a divisor of 4980)
4980 / 2 = 2490 (the remainder is 0, so 2 is a divisor of 4980)
4980 / 3 = 1660 (the remainder is 0, so 3 is a divisor of 4980)
...
4980 / 4979 = 1.0002008435429 (the remainder is 1, so 4979 is not a divisor of 4980)
4980 / 4980 = 1 (the remainder is 0, so 4980 is a divisor of 4980)

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 4980 (i.e. 70.569115057509). 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 $\frac{N}{d} = D$ )

4980 / 1 = 4980 (the remainder is 0, so 1 and 4980 are divisors of 4980)
4980 / 2 = 2490 (the remainder is 0, so 2 and 2490 are divisors of 4980)
4980 / 3 = 1660 (the remainder is 0, so 3 and 1660 are divisors of 4980)
...
4980 / 69 = 72.173913043478 (the remainder is 12, so 69 is not a divisor of 4980)
4980 / 70 = 71.142857142857 (the remainder is 10, so 70 is not a divisor of 4980)