What are the divisors of 2481?

1, 3, 827, 2481

There is a total of 4 positive divisors.
The sum of these divisors is 3312.
The arithmetic mean is 828.

4 odd divisors

1, 3, 827, 2481

How to compute the divisors of 2481?

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 2481 by each of the numbers from 1 to 2481 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)

2481 / 1 = 2481 (the remainder is 0, so 1 is a divisor of 2481)
2481 / 2 = 1240.5 (the remainder is 1, so 2 is not a divisor of 2481)
2481 / 3 = 827 (the remainder is 0, so 3 is a divisor of 2481)
...
2481 / 2480 = 1.0004032258065 (the remainder is 1, so 2480 is not a divisor of 2481)
2481 / 2481 = 1 (the remainder is 0, so 2481 is a divisor of 2481)

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 2481 (i.e. 49.809637621649). 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 $\frac{N}{d} = D$ )

2481 / 1 = 2481 (the remainder is 0, so 1 and 2481 are divisors of 2481)
2481 / 2 = 1240.5 (the remainder is 1, so 2 is not a divisor of 2481)
2481 / 3 = 827 (the remainder is 0, so 3 and 827 are divisors of 2481)
...
2481 / 48 = 51.6875 (the remainder is 33, so 48 is not a divisor of 2481)
2481 / 49 = 50.632653061224 (the remainder is 31, so 49 is not a divisor of 2481)