What are the divisors of 453?

1, 3, 151, 453

There is a total of 4 positive divisors.
The sum of these divisors is 608.
The arithmetic mean is 152.

4 odd divisors

1, 3, 151, 453

How to compute the divisors of 453?

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 453 by each of the numbers from 1 to 453 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)

453 / 1 = 453 (the remainder is 0, so 1 is a divisor of 453)
453 / 2 = 226.5 (the remainder is 1, so 2 is not a divisor of 453)
453 / 3 = 151 (the remainder is 0, so 3 is a divisor of 453)
...
453 / 452 = 1.0022123893805 (the remainder is 1, so 452 is not a divisor of 453)
453 / 453 = 1 (the remainder is 0, so 453 is a divisor of 453)

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 453 (i.e. 21.283796653793). 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 $\frac{N}{d} = D$ )

453 / 1 = 453 (the remainder is 0, so 1 and 453 are divisors of 453)
453 / 2 = 226.5 (the remainder is 1, so 2 is not a divisor of 453)
453 / 3 = 151 (the remainder is 0, so 3 and 151 are divisors of 453)
...
453 / 20 = 22.65 (the remainder is 13, so 20 is not a divisor of 453)
453 / 21 = 21.571428571429 (the remainder is 12, so 21 is not a divisor of 453)