What are the divisors of 1062?

1, 2, 3, 6, 9, 18, 59, 118, 177, 354, 531, 1062

There is a total of 12 positive divisors.
The sum of these divisors is 2340.
The arithmetic mean is 195.

6 even divisors

2, 6, 18, 118, 354, 1062

6 odd divisors

1, 3, 9, 59, 177, 531

How to compute the divisors of 1062?

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 1062 by each of the numbers from 1 to 1062 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)

1062 / 1 = 1062 (the remainder is 0, so 1 is a divisor of 1062)
1062 / 2 = 531 (the remainder is 0, so 2 is a divisor of 1062)
1062 / 3 = 354 (the remainder is 0, so 3 is a divisor of 1062)
...
1062 / 1061 = 1.0009425070688 (the remainder is 1, so 1061 is not a divisor of 1062)
1062 / 1062 = 1 (the remainder is 0, so 1062 is a divisor of 1062)

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 1062 (i.e. 32.588341473601). 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 $\frac{N}{d} = D$ )

1062 / 1 = 1062 (the remainder is 0, so 1 and 1062 are divisors of 1062)
1062 / 2 = 531 (the remainder is 0, so 2 and 531 are divisors of 1062)
1062 / 3 = 354 (the remainder is 0, so 3 and 354 are divisors of 1062)
...
1062 / 31 = 34.258064516129 (the remainder is 8, so 31 is not a divisor of 1062)
1062 / 32 = 33.1875 (the remainder is 6, so 32 is not a divisor of 1062)