What are the divisors of 2120?

1, 2, 4, 5, 8, 10, 20, 40, 53, 106, 212, 265, 424, 530, 1060, 2120

There is a total of 16 positive divisors.
The sum of these divisors is 4860.
The arithmetic mean is 303.75.

12 even divisors

2, 4, 8, 10, 20, 40, 106, 212, 424, 530, 1060, 2120

4 odd divisors

1, 5, 53, 265

How to compute the divisors of 2120?

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 2120 by each of the numbers from 1 to 2120 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)

2120 / 1 = 2120 (the remainder is 0, so 1 is a divisor of 2120)
2120 / 2 = 1060 (the remainder is 0, so 2 is a divisor of 2120)
2120 / 3 = 706.66666666667 (the remainder is 2, so 3 is not a divisor of 2120)
...
2120 / 2119 = 1.0004719207173 (the remainder is 1, so 2119 is not a divisor of 2120)
2120 / 2120 = 1 (the remainder is 0, so 2120 is a divisor of 2120)

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 2120 (i.e. 46.043457732885). 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 $\frac{N}{d} = D$ )

2120 / 1 = 2120 (the remainder is 0, so 1 and 2120 are divisors of 2120)
2120 / 2 = 1060 (the remainder is 0, so 2 and 1060 are divisors of 2120)
2120 / 3 = 706.66666666667 (the remainder is 2, so 3 is not a divisor of 2120)
...
2120 / 45 = 47.111111111111 (the remainder is 5, so 45 is not a divisor of 2120)
2120 / 46 = 46.086956521739 (the remainder is 4, so 46 is not a divisor of 2120)