What are the divisors of 470?

1, 2, 5, 10, 47, 94, 235, 470

There is a total of 8 positive divisors.
The sum of these divisors is 864.
The arithmetic mean is 108.

4 even divisors

2, 10, 94, 470

4 odd divisors

1, 5, 47, 235

How to compute the divisors of 470?

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 470 by each of the numbers from 1 to 470 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)

470 / 1 = 470 (the remainder is 0, so 1 is a divisor of 470)
470 / 2 = 235 (the remainder is 0, so 2 is a divisor of 470)
470 / 3 = 156.66666666667 (the remainder is 2, so 3 is not a divisor of 470)
...
470 / 469 = 1.002132196162 (the remainder is 1, so 469 is not a divisor of 470)
470 / 470 = 1 (the remainder is 0, so 470 is a divisor of 470)

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 470 (i.e. 21.679483388679). 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 $\frac{N}{d} = D$ )

470 / 1 = 470 (the remainder is 0, so 1 and 470 are divisors of 470)
470 / 2 = 235 (the remainder is 0, so 2 and 235 are divisors of 470)
470 / 3 = 156.66666666667 (the remainder is 2, so 3 is not a divisor of 470)
...
470 / 20 = 23.5 (the remainder is 10, so 20 is not a divisor of 470)
470 / 21 = 22.380952380952 (the remainder is 8, so 21 is not a divisor of 470)