What are the divisors of 430?

1, 2, 5, 10, 43, 86, 215, 430

There is a total of 8 positive divisors.
The sum of these divisors is 792.
The arithmetic mean is 99.

4 even divisors

2, 10, 86, 430

4 odd divisors

1, 5, 43, 215

How to compute the divisors of 430?

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 430 by each of the numbers from 1 to 430 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)

430 / 1 = 430 (the remainder is 0, so 1 is a divisor of 430)
430 / 2 = 215 (the remainder is 0, so 2 is a divisor of 430)
430 / 3 = 143.33333333333 (the remainder is 1, so 3 is not a divisor of 430)
...
430 / 429 = 1.002331002331 (the remainder is 1, so 429 is not a divisor of 430)
430 / 430 = 1 (the remainder is 0, so 430 is a divisor of 430)

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 430 (i.e. 20.736441353328). 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 $\frac{N}{d} = D$ )

430 / 1 = 430 (the remainder is 0, so 1 and 430 are divisors of 430)
430 / 2 = 215 (the remainder is 0, so 2 and 215 are divisors of 430)
430 / 3 = 143.33333333333 (the remainder is 1, so 3 is not a divisor of 430)
...
430 / 19 = 22.631578947368 (the remainder is 12, so 19 is not a divisor of 430)
430 / 20 = 21.5 (the remainder is 10, so 20 is not a divisor of 430)