What are the divisors of 882?

1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 49, 63, 98, 126, 147, 294, 441, 882

There is a total of 18 positive divisors.
The sum of these divisors is 2223.
The arithmetic mean is 123.5.

9 even divisors

2, 6, 14, 18, 42, 98, 126, 294, 882

9 odd divisors

1, 3, 7, 9, 21, 49, 63, 147, 441

How to compute the divisors of 882?

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 882 by each of the numbers from 1 to 882 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)

882 / 1 = 882 (the remainder is 0, so 1 is a divisor of 882)
882 / 2 = 441 (the remainder is 0, so 2 is a divisor of 882)
882 / 3 = 294 (the remainder is 0, so 3 is a divisor of 882)
...
882 / 881 = 1.0011350737798 (the remainder is 1, so 881 is not a divisor of 882)
882 / 882 = 1 (the remainder is 0, so 882 is a divisor of 882)

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 882 (i.e. 29.698484809835). 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 $\frac{N}{d} = D$ )

882 / 1 = 882 (the remainder is 0, so 1 and 882 are divisors of 882)
882 / 2 = 441 (the remainder is 0, so 2 and 441 are divisors of 882)
882 / 3 = 294 (the remainder is 0, so 3 and 294 are divisors of 882)
...
882 / 28 = 31.5 (the remainder is 14, so 28 is not a divisor of 882)
882 / 29 = 30.413793103448 (the remainder is 12, so 29 is not a divisor of 882)