What are the divisors of 476?

1, 2, 4, 7, 14, 17, 28, 34, 68, 119, 238, 476

There is a total of 12 positive divisors.
The sum of these divisors is 1008.
The arithmetic mean is 84.

8 even divisors

2, 4, 14, 28, 34, 68, 238, 476

4 odd divisors

1, 7, 17, 119

How to compute the divisors of 476?

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 476 by each of the numbers from 1 to 476 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)

476 / 1 = 476 (the remainder is 0, so 1 is a divisor of 476)
476 / 2 = 238 (the remainder is 0, so 2 is a divisor of 476)
476 / 3 = 158.66666666667 (the remainder is 2, so 3 is not a divisor of 476)
...
476 / 475 = 1.0021052631579 (the remainder is 1, so 475 is not a divisor of 476)
476 / 476 = 1 (the remainder is 0, so 476 is a divisor of 476)

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 476 (i.e. 21.817424229271). 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 $\frac{N}{d} = D$ )

476 / 1 = 476 (the remainder is 0, so 1 and 476 are divisors of 476)
476 / 2 = 238 (the remainder is 0, so 2 and 238 are divisors of 476)
476 / 3 = 158.66666666667 (the remainder is 2, so 3 is not a divisor of 476)
...
476 / 20 = 23.8 (the remainder is 16, so 20 is not a divisor of 476)
476 / 21 = 22.666666666667 (the remainder is 14, so 21 is not a divisor of 476)