What are the divisors of 479?

1, 479

There is a total of 2 positive divisors.
The sum of these divisors is 480.
The arithmetic mean is 240.

2 odd divisors

1, 479

How to compute the divisors of 479?

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 479 by each of the numbers from 1 to 479 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)

479 / 1 = 479 (the remainder is 0, so 1 is a divisor of 479)
479 / 2 = 239.5 (the remainder is 1, so 2 is not a divisor of 479)
479 / 3 = 159.66666666667 (the remainder is 2, so 3 is not a divisor of 479)
...
479 / 478 = 1.0020920502092 (the remainder is 1, so 478 is not a divisor of 479)
479 / 479 = 1 (the remainder is 0, so 479 is a divisor of 479)

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 479 (i.e. 21.886068628239). 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 $\frac{N}{d} = D$ )

479 / 1 = 479 (the remainder is 0, so 1 and 479 are divisors of 479)
479 / 2 = 239.5 (the remainder is 1, so 2 is not a divisor of 479)
479 / 3 = 159.66666666667 (the remainder is 2, so 3 is not a divisor of 479)
...
479 / 20 = 23.95 (the remainder is 19, so 20 is not a divisor of 479)
479 / 21 = 22.809523809524 (the remainder is 17, so 21 is not a divisor of 479)