What are the divisors of 1316?

1, 2, 4, 7, 14, 28, 47, 94, 188, 329, 658, 1316

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, 14, 28, 94, 188, 658, 1316

4 odd divisors

1, 7, 47, 329

How to compute the divisors of 1316?

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 1316 by each of the numbers from 1 to 1316 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)

1316 / 1 = 1316 (the remainder is 0, so 1 is a divisor of 1316)
1316 / 2 = 658 (the remainder is 0, so 2 is a divisor of 1316)
1316 / 3 = 438.66666666667 (the remainder is 2, so 3 is not a divisor of 1316)
...
1316 / 1315 = 1.0007604562738 (the remainder is 1, so 1315 is not a divisor of 1316)
1316 / 1316 = 1 (the remainder is 0, so 1316 is a divisor of 1316)

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 1316 (i.e. 36.276714294434). 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 $\frac{N}{d} = D$ )

1316 / 1 = 1316 (the remainder is 0, so 1 and 1316 are divisors of 1316)
1316 / 2 = 658 (the remainder is 0, so 2 and 658 are divisors of 1316)
1316 / 3 = 438.66666666667 (the remainder is 2, so 3 is not a divisor of 1316)
...
1316 / 35 = 37.6 (the remainder is 21, so 35 is not a divisor of 1316)
1316 / 36 = 36.555555555556 (the remainder is 20, so 36 is not a divisor of 1316)