What are the divisors of 478?

1, 2, 239, 478

There is a total of 4 positive divisors.
The sum of these divisors is 720.
The arithmetic mean is 180.

2 even divisors

2, 478

2 odd divisors

1, 239

How to compute the divisors of 478?

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 478 by each of the numbers from 1 to 478 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)

478 / 1 = 478 (the remainder is 0, so 1 is a divisor of 478)
478 / 2 = 239 (the remainder is 0, so 2 is a divisor of 478)
478 / 3 = 159.33333333333 (the remainder is 1, so 3 is not a divisor of 478)
...
478 / 477 = 1.0020964360587 (the remainder is 1, so 477 is not a divisor of 478)
478 / 478 = 1 (the remainder is 0, so 478 is a divisor of 478)

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 478 (i.e. 21.863211109075). 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 $\frac{N}{d} = D$ )

478 / 1 = 478 (the remainder is 0, so 1 and 478 are divisors of 478)
478 / 2 = 239 (the remainder is 0, so 2 and 239 are divisors of 478)
478 / 3 = 159.33333333333 (the remainder is 1, so 3 is not a divisor of 478)
...
478 / 20 = 23.9 (the remainder is 18, so 20 is not a divisor of 478)
478 / 21 = 22.761904761905 (the remainder is 16, so 21 is not a divisor of 478)