What are the divisors of 2121?

1, 3, 7, 21, 101, 303, 707, 2121

There is a total of 8 positive divisors.
The sum of these divisors is 3264.
The arithmetic mean is 408.

8 odd divisors

1, 3, 7, 21, 101, 303, 707, 2121

How to compute the divisors of 2121?

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 2121 by each of the numbers from 1 to 2121 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)

2121 / 1 = 2121 (the remainder is 0, so 1 is a divisor of 2121)
2121 / 2 = 1060.5 (the remainder is 1, so 2 is not a divisor of 2121)
2121 / 3 = 707 (the remainder is 0, so 3 is a divisor of 2121)
...
2121 / 2120 = 1.0004716981132 (the remainder is 1, so 2120 is not a divisor of 2121)
2121 / 2121 = 1 (the remainder is 0, so 2121 is a divisor of 2121)

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 2121 (i.e. 46.054315758678). 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 $\frac{N}{d} = D$ )

2121 / 1 = 2121 (the remainder is 0, so 1 and 2121 are divisors of 2121)
2121 / 2 = 1060.5 (the remainder is 1, so 2 is not a divisor of 2121)
2121 / 3 = 707 (the remainder is 0, so 3 and 707 are divisors of 2121)
...
2121 / 45 = 47.133333333333 (the remainder is 6, so 45 is not a divisor of 2121)
2121 / 46 = 46.108695652174 (the remainder is 5, so 46 is not a divisor of 2121)