What are the divisors of 1360?

1, 2, 4, 5, 8, 10, 16, 17, 20, 34, 40, 68, 80, 85, 136, 170, 272, 340, 680, 1360

There is a total of 20 positive divisors.
The sum of these divisors is 3348.
The arithmetic mean is 167.4.

16 even divisors

2, 4, 8, 10, 16, 20, 34, 40, 68, 80, 136, 170, 272, 340, 680, 1360

4 odd divisors

1, 5, 17, 85

How to compute the divisors of 1360?

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 1360 by each of the numbers from 1 to 1360 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)

1360 / 1 = 1360 (the remainder is 0, so 1 is a divisor of 1360)
1360 / 2 = 680 (the remainder is 0, so 2 is a divisor of 1360)
1360 / 3 = 453.33333333333 (the remainder is 1, so 3 is not a divisor of 1360)
...
1360 / 1359 = 1.0007358351729 (the remainder is 1, so 1359 is not a divisor of 1360)
1360 / 1360 = 1 (the remainder is 0, so 1360 is a divisor of 1360)

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 1360 (i.e. 36.878177829172). 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 $\frac{N}{d} = D$ )

1360 / 1 = 1360 (the remainder is 0, so 1 and 1360 are divisors of 1360)
1360 / 2 = 680 (the remainder is 0, so 2 and 680 are divisors of 1360)
1360 / 3 = 453.33333333333 (the remainder is 1, so 3 is not a divisor of 1360)
...
1360 / 35 = 38.857142857143 (the remainder is 30, so 35 is not a divisor of 1360)
1360 / 36 = 37.777777777778 (the remainder is 28, so 36 is not a divisor of 1360)