What are the divisors of 454?

1, 2, 227, 454

There is a total of 4 positive divisors.
The sum of these divisors is 684.
The arithmetic mean is 171.

2 even divisors

2, 454

2 odd divisors

1, 227

How to compute the divisors of 454?

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 454 by each of the numbers from 1 to 454 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)

454 / 1 = 454 (the remainder is 0, so 1 is a divisor of 454)
454 / 2 = 227 (the remainder is 0, so 2 is a divisor of 454)
454 / 3 = 151.33333333333 (the remainder is 1, so 3 is not a divisor of 454)
...
454 / 453 = 1.0022075055188 (the remainder is 1, so 453 is not a divisor of 454)
454 / 454 = 1 (the remainder is 0, so 454 is a divisor of 454)

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 454 (i.e. 21.307275752663). 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 $\frac{N}{d} = D$ )

454 / 1 = 454 (the remainder is 0, so 1 and 454 are divisors of 454)
454 / 2 = 227 (the remainder is 0, so 2 and 227 are divisors of 454)
454 / 3 = 151.33333333333 (the remainder is 1, so 3 is not a divisor of 454)
...
454 / 20 = 22.7 (the remainder is 14, so 20 is not a divisor of 454)
454 / 21 = 21.619047619048 (the remainder is 13, so 21 is not a divisor of 454)