What are the divisors of 2397?

1, 3, 17, 47, 51, 141, 799, 2397

There is a total of 8 positive divisors.
The sum of these divisors is 3456.
The arithmetic mean is 432.

8 odd divisors

1, 3, 17, 47, 51, 141, 799, 2397

How to compute the divisors of 2397?

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 2397 by each of the numbers from 1 to 2397 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)

2397 / 1 = 2397 (the remainder is 0, so 1 is a divisor of 2397)
2397 / 2 = 1198.5 (the remainder is 1, so 2 is not a divisor of 2397)
2397 / 3 = 799 (the remainder is 0, so 3 is a divisor of 2397)
...
2397 / 2396 = 1.0004173622705 (the remainder is 1, so 2396 is not a divisor of 2397)
2397 / 2397 = 1 (the remainder is 0, so 2397 is a divisor of 2397)

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 2397 (i.e. 48.959166659575). 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 $\frac{N}{d} = D$ )

2397 / 1 = 2397 (the remainder is 0, so 1 and 2397 are divisors of 2397)
2397 / 2 = 1198.5 (the remainder is 1, so 2 is not a divisor of 2397)
2397 / 3 = 799 (the remainder is 0, so 3 and 799 are divisors of 2397)
...
2397 / 47 = 51 (the remainder is 0, so 47 and 51 are divisors of 2397)
2397 / 48 = 49.9375 (the remainder is 45, so 48 is not a divisor of 2397)