What are the divisors of 2435?

1, 5, 487, 2435

There is a total of 4 positive divisors.
The sum of these divisors is 2928.
The arithmetic mean is 732.

4 odd divisors

1, 5, 487, 2435

How to compute the divisors of 2435?

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 2435 by each of the numbers from 1 to 2435 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)

2435 / 1 = 2435 (the remainder is 0, so 1 is a divisor of 2435)
2435 / 2 = 1217.5 (the remainder is 1, so 2 is not a divisor of 2435)
2435 / 3 = 811.66666666667 (the remainder is 2, so 3 is not a divisor of 2435)
...
2435 / 2434 = 1.0004108463435 (the remainder is 1, so 2434 is not a divisor of 2435)
2435 / 2435 = 1 (the remainder is 0, so 2435 is a divisor of 2435)

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 2435 (i.e. 49.345719165901). 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 $\frac{N}{d} = D$ )

2435 / 1 = 2435 (the remainder is 0, so 1 and 2435 are divisors of 2435)
2435 / 2 = 1217.5 (the remainder is 1, so 2 is not a divisor of 2435)
2435 / 3 = 811.66666666667 (the remainder is 2, so 3 is not a divisor of 2435)
...
2435 / 48 = 50.729166666667 (the remainder is 35, so 48 is not a divisor of 2435)
2435 / 49 = 49.69387755102 (the remainder is 34, so 49 is not a divisor of 2435)