What are the divisors of 446?

1, 2, 223, 446

There is a total of 4 positive divisors.
The sum of these divisors is 672.
The arithmetic mean is 168.

2 even divisors

2, 446

2 odd divisors

1, 223

How to compute the divisors of 446?

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 446 by each of the numbers from 1 to 446 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)

446 / 1 = 446 (the remainder is 0, so 1 is a divisor of 446)
446 / 2 = 223 (the remainder is 0, so 2 is a divisor of 446)
446 / 3 = 148.66666666667 (the remainder is 2, so 3 is not a divisor of 446)
...
446 / 445 = 1.0022471910112 (the remainder is 1, so 445 is not a divisor of 446)
446 / 446 = 1 (the remainder is 0, so 446 is a divisor of 446)

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 446 (i.e. 21.118712081943). 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 $\frac{N}{d} = D$ )

446 / 1 = 446 (the remainder is 0, so 1 and 446 are divisors of 446)
446 / 2 = 223 (the remainder is 0, so 2 and 223 are divisors of 446)
446 / 3 = 148.66666666667 (the remainder is 2, so 3 is not a divisor of 446)
...
446 / 20 = 22.3 (the remainder is 6, so 20 is not a divisor of 446)
446 / 21 = 21.238095238095 (the remainder is 5, so 21 is not a divisor of 446)