What are the divisors of 451?

1, 11, 41, 451

There is a total of 4 positive divisors.
The sum of these divisors is 504.
The arithmetic mean is 126.

4 odd divisors

1, 11, 41, 451

How to compute the divisors of 451?

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 451 by each of the numbers from 1 to 451 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)

451 / 1 = 451 (the remainder is 0, so 1 is a divisor of 451)
451 / 2 = 225.5 (the remainder is 1, so 2 is not a divisor of 451)
451 / 3 = 150.33333333333 (the remainder is 1, so 3 is not a divisor of 451)
...
451 / 450 = 1.0022222222222 (the remainder is 1, so 450 is not a divisor of 451)
451 / 451 = 1 (the remainder is 0, so 451 is a divisor of 451)

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 451 (i.e. 21.236760581595). 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 $\frac{N}{d} = D$ )

451 / 1 = 451 (the remainder is 0, so 1 and 451 are divisors of 451)
451 / 2 = 225.5 (the remainder is 1, so 2 is not a divisor of 451)
451 / 3 = 150.33333333333 (the remainder is 1, so 3 is not a divisor of 451)
...
451 / 20 = 22.55 (the remainder is 11, so 20 is not a divisor of 451)
451 / 21 = 21.47619047619 (the remainder is 10, so 21 is not a divisor of 451)