What are the divisors of 1072?

1, 2, 4, 8, 16, 67, 134, 268, 536, 1072

There is a total of 10 positive divisors.
The sum of these divisors is 2108.
The arithmetic mean is 210.8.

8 even divisors

2, 4, 8, 16, 134, 268, 536, 1072

2 odd divisors

1, 67

How to compute the divisors of 1072?

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 1072 by each of the numbers from 1 to 1072 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)

1072 / 1 = 1072 (the remainder is 0, so 1 is a divisor of 1072)
1072 / 2 = 536 (the remainder is 0, so 2 is a divisor of 1072)
1072 / 3 = 357.33333333333 (the remainder is 1, so 3 is not a divisor of 1072)
...
1072 / 1071 = 1.0009337068161 (the remainder is 1, so 1071 is not a divisor of 1072)
1072 / 1072 = 1 (the remainder is 0, so 1072 is a divisor of 1072)

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 1072 (i.e. 32.74141108749). 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 $\frac{N}{d} = D$ )

1072 / 1 = 1072 (the remainder is 0, so 1 and 1072 are divisors of 1072)
1072 / 2 = 536 (the remainder is 0, so 2 and 536 are divisors of 1072)
1072 / 3 = 357.33333333333 (the remainder is 1, so 3 is not a divisor of 1072)
...
1072 / 31 = 34.58064516129 (the remainder is 18, so 31 is not a divisor of 1072)
1072 / 32 = 33.5 (the remainder is 16, so 32 is not a divisor of 1072)