What are the divisors of 1064?

1, 2, 4, 7, 8, 14, 19, 28, 38, 56, 76, 133, 152, 266, 532, 1064

There is a total of 16 positive divisors.
The sum of these divisors is 2400.
The arithmetic mean is 150.

12 even divisors

2, 4, 8, 14, 28, 38, 56, 76, 152, 266, 532, 1064

4 odd divisors

1, 7, 19, 133

How to compute the divisors of 1064?

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 1064 by each of the numbers from 1 to 1064 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)

1064 / 1 = 1064 (the remainder is 0, so 1 is a divisor of 1064)
1064 / 2 = 532 (the remainder is 0, so 2 is a divisor of 1064)
1064 / 3 = 354.66666666667 (the remainder is 2, so 3 is not a divisor of 1064)
...
1064 / 1063 = 1.0009407337723 (the remainder is 1, so 1063 is not a divisor of 1064)
1064 / 1064 = 1 (the remainder is 0, so 1064 is a divisor of 1064)

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 1064 (i.e. 32.6190128606). 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 $\frac{N}{d} = D$ )

1064 / 1 = 1064 (the remainder is 0, so 1 and 1064 are divisors of 1064)
1064 / 2 = 532 (the remainder is 0, so 2 and 532 are divisors of 1064)
1064 / 3 = 354.66666666667 (the remainder is 2, so 3 is not a divisor of 1064)
...
1064 / 31 = 34.322580645161 (the remainder is 10, so 31 is not a divisor of 1064)
1064 / 32 = 33.25 (the remainder is 8, so 32 is not a divisor of 1064)