What are the divisors of 475?

1, 5, 19, 25, 95, 475

There is a total of 6 positive divisors.
The sum of these divisors is 620.
The arithmetic mean is 103.33333333333.

6 odd divisors

1, 5, 19, 25, 95, 475

How to compute the divisors of 475?

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 475 by each of the numbers from 1 to 475 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)

475 / 1 = 475 (the remainder is 0, so 1 is a divisor of 475)
475 / 2 = 237.5 (the remainder is 1, so 2 is not a divisor of 475)
475 / 3 = 158.33333333333 (the remainder is 1, so 3 is not a divisor of 475)
...
475 / 474 = 1.0021097046414 (the remainder is 1, so 474 is not a divisor of 475)
475 / 475 = 1 (the remainder is 0, so 475 is a divisor of 475)

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 475 (i.e. 21.794494717703). 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 $\frac{N}{d} = D$ )

475 / 1 = 475 (the remainder is 0, so 1 and 475 are divisors of 475)
475 / 2 = 237.5 (the remainder is 1, so 2 is not a divisor of 475)
475 / 3 = 158.33333333333 (the remainder is 1, so 3 is not a divisor of 475)
...
475 / 20 = 23.75 (the remainder is 15, so 20 is not a divisor of 475)
475 / 21 = 22.619047619048 (the remainder is 13, so 21 is not a divisor of 475)