What are the divisors of 1302?

1, 2, 3, 6, 7, 14, 21, 31, 42, 62, 93, 186, 217, 434, 651, 1302

There is a total of 16 positive divisors.
The sum of these divisors is 3072.
The arithmetic mean is 192.

8 even divisors

2, 6, 14, 42, 62, 186, 434, 1302

8 odd divisors

1, 3, 7, 21, 31, 93, 217, 651

How to compute the divisors of 1302?

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 1302 by each of the numbers from 1 to 1302 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)

1302 / 1 = 1302 (the remainder is 0, so 1 is a divisor of 1302)
1302 / 2 = 651 (the remainder is 0, so 2 is a divisor of 1302)
1302 / 3 = 434 (the remainder is 0, so 3 is a divisor of 1302)
...
1302 / 1301 = 1.0007686395081 (the remainder is 1, so 1301 is not a divisor of 1302)
1302 / 1302 = 1 (the remainder is 0, so 1302 is a divisor of 1302)

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 1302 (i.e. 36.083237105337). 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 $\frac{N}{d} = D$ )

1302 / 1 = 1302 (the remainder is 0, so 1 and 1302 are divisors of 1302)
1302 / 2 = 651 (the remainder is 0, so 2 and 651 are divisors of 1302)
1302 / 3 = 434 (the remainder is 0, so 3 and 434 are divisors of 1302)
...
1302 / 35 = 37.2 (the remainder is 7, so 35 is not a divisor of 1302)
1302 / 36 = 36.166666666667 (the remainder is 6, so 36 is not a divisor of 1302)