What are the divisors of 442?

1, 2, 13, 17, 26, 34, 221, 442

There is a total of 8 positive divisors.
The sum of these divisors is 756.
The arithmetic mean is 94.5.

4 even divisors

2, 26, 34, 442

4 odd divisors

1, 13, 17, 221

How to compute the divisors of 442?

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 442 by each of the numbers from 1 to 442 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)

442 / 1 = 442 (the remainder is 0, so 1 is a divisor of 442)
442 / 2 = 221 (the remainder is 0, so 2 is a divisor of 442)
442 / 3 = 147.33333333333 (the remainder is 1, so 3 is not a divisor of 442)
...
442 / 441 = 1.0022675736961 (the remainder is 1, so 441 is not a divisor of 442)
442 / 442 = 1 (the remainder is 0, so 442 is a divisor of 442)

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 442 (i.e. 21.023796041629). 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 $\frac{N}{d} = D$ )

442 / 1 = 442 (the remainder is 0, so 1 and 442 are divisors of 442)
442 / 2 = 221 (the remainder is 0, so 2 and 221 are divisors of 442)
442 / 3 = 147.33333333333 (the remainder is 1, so 3 is not a divisor of 442)
...
442 / 20 = 22.1 (the remainder is 2, so 20 is not a divisor of 442)
442 / 21 = 21.047619047619 (the remainder is 1, so 21 is not a divisor of 442)