What are the divisors of 2434?

1, 2, 1217, 2434

There is a total of 4 positive divisors.
The sum of these divisors is 3654.
The arithmetic mean is 913.5.

2 even divisors

2, 2434

2 odd divisors

1, 1217

How to compute the divisors of 2434?

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 2434 by each of the numbers from 1 to 2434 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)

2434 / 1 = 2434 (the remainder is 0, so 1 is a divisor of 2434)
2434 / 2 = 1217 (the remainder is 0, so 2 is a divisor of 2434)
2434 / 3 = 811.33333333333 (the remainder is 1, so 3 is not a divisor of 2434)
...
2434 / 2433 = 1.0004110152076 (the remainder is 1, so 2433 is not a divisor of 2434)
2434 / 2434 = 1 (the remainder is 0, so 2434 is a divisor of 2434)

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 2434 (i.e. 49.335585534176). 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 $\frac{N}{d} = D$ )

2434 / 1 = 2434 (the remainder is 0, so 1 and 2434 are divisors of 2434)
2434 / 2 = 1217 (the remainder is 0, so 2 and 1217 are divisors of 2434)
2434 / 3 = 811.33333333333 (the remainder is 1, so 3 is not a divisor of 2434)
...
2434 / 48 = 50.708333333333 (the remainder is 34, so 48 is not a divisor of 2434)
2434 / 49 = 49.673469387755 (the remainder is 33, so 49 is not a divisor of 2434)