What are the divisors of 488?

1, 2, 4, 8, 61, 122, 244, 488

There is a total of 8 positive divisors.
The sum of these divisors is 930.
The arithmetic mean is 116.25.

6 even divisors

2, 4, 8, 122, 244, 488

2 odd divisors

1, 61

How to compute the divisors of 488?

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 488 by each of the numbers from 1 to 488 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)

488 / 1 = 488 (the remainder is 0, so 1 is a divisor of 488)
488 / 2 = 244 (the remainder is 0, so 2 is a divisor of 488)
488 / 3 = 162.66666666667 (the remainder is 2, so 3 is not a divisor of 488)
...
488 / 487 = 1.0020533880903 (the remainder is 1, so 487 is not a divisor of 488)
488 / 488 = 1 (the remainder is 0, so 488 is a divisor of 488)

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 488 (i.e. 22.090722034375). 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 $\frac{N}{d} = D$ )

488 / 1 = 488 (the remainder is 0, so 1 and 488 are divisors of 488)
488 / 2 = 244 (the remainder is 0, so 2 and 244 are divisors of 488)
488 / 3 = 162.66666666667 (the remainder is 2, so 3 is not a divisor of 488)
...
488 / 21 = 23.238095238095 (the remainder is 5, so 21 is not a divisor of 488)
488 / 22 = 22.181818181818 (the remainder is 4, so 22 is not a divisor of 488)