What are the divisors of 463?

1, 463

There is a total of 2 positive divisors.
The sum of these divisors is 464.
The arithmetic mean is 232.

2 odd divisors

1, 463

How to compute the divisors of 463?

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 463 by each of the numbers from 1 to 463 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)

463 / 1 = 463 (the remainder is 0, so 1 is a divisor of 463)
463 / 2 = 231.5 (the remainder is 1, so 2 is not a divisor of 463)
463 / 3 = 154.33333333333 (the remainder is 1, so 3 is not a divisor of 463)
...
463 / 462 = 1.0021645021645 (the remainder is 1, so 462 is not a divisor of 463)
463 / 463 = 1 (the remainder is 0, so 463 is a divisor of 463)

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 463 (i.e. 21.51743479135). 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 $\frac{N}{d} = D$ )

463 / 1 = 463 (the remainder is 0, so 1 and 463 are divisors of 463)
463 / 2 = 231.5 (the remainder is 1, so 2 is not a divisor of 463)
463 / 3 = 154.33333333333 (the remainder is 1, so 3 is not a divisor of 463)
...
463 / 20 = 23.15 (the remainder is 3, so 20 is not a divisor of 463)
463 / 21 = 22.047619047619 (the remainder is 1, so 21 is not a divisor of 463)