What are the divisors of 3008?

1, 2, 4, 8, 16, 32, 47, 64, 94, 188, 376, 752, 1504, 3008

There is a total of 14 positive divisors.
The sum of these divisors is 6096.
The arithmetic mean is 435.42857142857.

12 even divisors

2, 4, 8, 16, 32, 64, 94, 188, 376, 752, 1504, 3008

2 odd divisors

1, 47

How to compute the divisors of 3008?

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 3008 by each of the numbers from 1 to 3008 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)

3008 / 1 = 3008 (the remainder is 0, so 1 is a divisor of 3008)
3008 / 2 = 1504 (the remainder is 0, so 2 is a divisor of 3008)
3008 / 3 = 1002.6666666667 (the remainder is 2, so 3 is not a divisor of 3008)
...
3008 / 3007 = 1.0003325573661 (the remainder is 1, so 3007 is not a divisor of 3008)
3008 / 3008 = 1 (the remainder is 0, so 3008 is a divisor of 3008)

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 3008 (i.e. 54.845236803208). 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 $\frac{N}{d} = D$ )

3008 / 1 = 3008 (the remainder is 0, so 1 and 3008 are divisors of 3008)
3008 / 2 = 1504 (the remainder is 0, so 2 and 1504 are divisors of 3008)
3008 / 3 = 1002.6666666667 (the remainder is 2, so 3 is not a divisor of 3008)
...
3008 / 53 = 56.754716981132 (the remainder is 40, so 53 is not a divisor of 3008)
3008 / 54 = 55.703703703704 (the remainder is 38, so 54 is not a divisor of 3008)