What are the divisors of 1063?

1, 1063

There is a total of 2 positive divisors.
The sum of these divisors is 1064.
The arithmetic mean is 532.

2 odd divisors

1, 1063

How to compute the divisors of 1063?

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 1063 by each of the numbers from 1 to 1063 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)

1063 / 1 = 1063 (the remainder is 0, so 1 is a divisor of 1063)
1063 / 2 = 531.5 (the remainder is 1, so 2 is not a divisor of 1063)
1063 / 3 = 354.33333333333 (the remainder is 1, so 3 is not a divisor of 1063)
...
1063 / 1062 = 1.0009416195857 (the remainder is 1, so 1062 is not a divisor of 1063)
1063 / 1063 = 1 (the remainder is 0, so 1063 is a divisor of 1063)

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 1063 (i.e. 32.603680773802). 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 $\frac{N}{d} = D$ )

1063 / 1 = 1063 (the remainder is 0, so 1 and 1063 are divisors of 1063)
1063 / 2 = 531.5 (the remainder is 1, so 2 is not a divisor of 1063)
1063 / 3 = 354.33333333333 (the remainder is 1, so 3 is not a divisor of 1063)
...
1063 / 31 = 34.290322580645 (the remainder is 9, so 31 is not a divisor of 1063)
1063 / 32 = 33.21875 (the remainder is 7, so 32 is not a divisor of 1063)