What are the divisors of 842?

1, 2, 421, 842

There is a total of 4 positive divisors.
The sum of these divisors is 1266.
The arithmetic mean is 316.5.

2 even divisors

2, 842

2 odd divisors

1, 421

How to compute the divisors of 842?

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 842 by each of the numbers from 1 to 842 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)

842 / 1 = 842 (the remainder is 0, so 1 is a divisor of 842)
842 / 2 = 421 (the remainder is 0, so 2 is a divisor of 842)
842 / 3 = 280.66666666667 (the remainder is 2, so 3 is not a divisor of 842)
...
842 / 841 = 1.0011890606421 (the remainder is 1, so 841 is not a divisor of 842)
842 / 842 = 1 (the remainder is 0, so 842 is a divisor of 842)

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 842 (i.e. 29.017236257094). 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 $\frac{N}{d} = D$ )

842 / 1 = 842 (the remainder is 0, so 1 and 842 are divisors of 842)
842 / 2 = 421 (the remainder is 0, so 2 and 421 are divisors of 842)
842 / 3 = 280.66666666667 (the remainder is 2, so 3 is not a divisor of 842)
...
842 / 28 = 30.071428571429 (the remainder is 2, so 28 is not a divisor of 842)
842 / 29 = 29.034482758621 (the remainder is 1, so 29 is not a divisor of 842)