What are the divisors of 2421?

1, 3, 9, 269, 807, 2421

There is a total of 6 positive divisors.
The sum of these divisors is 3510.
The arithmetic mean is 585.

6 odd divisors

1, 3, 9, 269, 807, 2421

How to compute the divisors of 2421?

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 2421 by each of the numbers from 1 to 2421 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)

2421 / 1 = 2421 (the remainder is 0, so 1 is a divisor of 2421)
2421 / 2 = 1210.5 (the remainder is 1, so 2 is not a divisor of 2421)
2421 / 3 = 807 (the remainder is 0, so 3 is a divisor of 2421)
...
2421 / 2420 = 1.0004132231405 (the remainder is 1, so 2420 is not a divisor of 2421)
2421 / 2421 = 1 (the remainder is 0, so 2421 is a divisor of 2421)

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 2421 (i.e. 49.20365840057). 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 $\frac{N}{d} = D$ )

2421 / 1 = 2421 (the remainder is 0, so 1 and 2421 are divisors of 2421)
2421 / 2 = 1210.5 (the remainder is 1, so 2 is not a divisor of 2421)
2421 / 3 = 807 (the remainder is 0, so 3 and 807 are divisors of 2421)
...
2421 / 48 = 50.4375 (the remainder is 21, so 48 is not a divisor of 2421)
2421 / 49 = 49.408163265306 (the remainder is 20, so 49 is not a divisor of 2421)