What are the divisors of 1347?

1, 3, 449, 1347

There is a total of 4 positive divisors.
The sum of these divisors is 1800.
The arithmetic mean is 450.

4 odd divisors

1, 3, 449, 1347

How to compute the divisors of 1347?

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 1347 by each of the numbers from 1 to 1347 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)

1347 / 1 = 1347 (the remainder is 0, so 1 is a divisor of 1347)
1347 / 2 = 673.5 (the remainder is 1, so 2 is not a divisor of 1347)
1347 / 3 = 449 (the remainder is 0, so 3 is a divisor of 1347)
...
1347 / 1346 = 1.0007429420505 (the remainder is 1, so 1346 is not a divisor of 1347)
1347 / 1347 = 1 (the remainder is 0, so 1347 is a divisor of 1347)

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 1347 (i.e. 36.701498607005). 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 $\frac{N}{d} = D$ )

1347 / 1 = 1347 (the remainder is 0, so 1 and 1347 are divisors of 1347)
1347 / 2 = 673.5 (the remainder is 1, so 2 is not a divisor of 1347)
1347 / 3 = 449 (the remainder is 0, so 3 and 449 are divisors of 1347)
...
1347 / 35 = 38.485714285714 (the remainder is 17, so 35 is not a divisor of 1347)
1347 / 36 = 37.416666666667 (the remainder is 15, so 36 is not a divisor of 1347)