What are the divisors of 848?

1, 2, 4, 8, 16, 53, 106, 212, 424, 848

There is a total of 10 positive divisors.
The sum of these divisors is 1674.
The arithmetic mean is 167.4.

8 even divisors

2, 4, 8, 16, 106, 212, 424, 848

2 odd divisors

1, 53

How to compute the divisors of 848?

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 848 by each of the numbers from 1 to 848 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)

848 / 1 = 848 (the remainder is 0, so 1 is a divisor of 848)
848 / 2 = 424 (the remainder is 0, so 2 is a divisor of 848)
848 / 3 = 282.66666666667 (the remainder is 2, so 3 is not a divisor of 848)
...
848 / 847 = 1.0011806375443 (the remainder is 1, so 847 is not a divisor of 848)
848 / 848 = 1 (the remainder is 0, so 848 is a divisor of 848)

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 848 (i.e. 29.120439557122). 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 $\frac{N}{d} = D$ )

848 / 1 = 848 (the remainder is 0, so 1 and 848 are divisors of 848)
848 / 2 = 424 (the remainder is 0, so 2 and 424 are divisors of 848)
848 / 3 = 282.66666666667 (the remainder is 2, so 3 is not a divisor of 848)
...
848 / 28 = 30.285714285714 (the remainder is 8, so 28 is not a divisor of 848)
848 / 29 = 29.241379310345 (the remainder is 7, so 29 is not a divisor of 848)