What are the divisors of 1364?

1, 2, 4, 11, 22, 31, 44, 62, 124, 341, 682, 1364

There is a total of 12 positive divisors.
The sum of these divisors is 2688.
The arithmetic mean is 224.

8 even divisors

2, 4, 22, 44, 62, 124, 682, 1364

4 odd divisors

1, 11, 31, 341

How to compute the divisors of 1364?

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 1364 by each of the numbers from 1 to 1364 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)

1364 / 1 = 1364 (the remainder is 0, so 1 is a divisor of 1364)
1364 / 2 = 682 (the remainder is 0, so 2 is a divisor of 1364)
1364 / 3 = 454.66666666667 (the remainder is 2, so 3 is not a divisor of 1364)
...
1364 / 1363 = 1.0007336757153 (the remainder is 1, so 1363 is not a divisor of 1364)
1364 / 1364 = 1 (the remainder is 0, so 1364 is a divisor of 1364)

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 1364 (i.e. 36.932370625239). 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 $\frac{N}{d} = D$ )

1364 / 1 = 1364 (the remainder is 0, so 1 and 1364 are divisors of 1364)
1364 / 2 = 682 (the remainder is 0, so 2 and 682 are divisors of 1364)
1364 / 3 = 454.66666666667 (the remainder is 2, so 3 is not a divisor of 1364)
...
1364 / 35 = 38.971428571429 (the remainder is 34, so 35 is not a divisor of 1364)
1364 / 36 = 37.888888888889 (the remainder is 32, so 36 is not a divisor of 1364)