What are the divisors of 452?

1, 2, 4, 113, 226, 452

There is a total of 6 positive divisors.
The sum of these divisors is 798.
The arithmetic mean is 133.

4 even divisors

2, 4, 226, 452

2 odd divisors

1, 113

How to compute the divisors of 452?

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 452 by each of the numbers from 1 to 452 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)

452 / 1 = 452 (the remainder is 0, so 1 is a divisor of 452)
452 / 2 = 226 (the remainder is 0, so 2 is a divisor of 452)
452 / 3 = 150.66666666667 (the remainder is 2, so 3 is not a divisor of 452)
...
452 / 451 = 1.0022172949002 (the remainder is 1, so 451 is not a divisor of 452)
452 / 452 = 1 (the remainder is 0, so 452 is a divisor of 452)

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 452 (i.e. 21.260291625469). 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 $\frac{N}{d} = D$ )

452 / 1 = 452 (the remainder is 0, so 1 and 452 are divisors of 452)
452 / 2 = 226 (the remainder is 0, so 2 and 226 are divisors of 452)
452 / 3 = 150.66666666667 (the remainder is 2, so 3 is not a divisor of 452)
...
452 / 20 = 22.6 (the remainder is 12, so 20 is not a divisor of 452)
452 / 21 = 21.52380952381 (the remainder is 11, so 21 is not a divisor of 452)