What are the divisors of 3817?

1, 11, 347, 3817

There is a total of 4 positive divisors.
The sum of these divisors is 4176.
The arithmetic mean is 1044.

4 odd divisors

1, 11, 347, 3817

How to compute the divisors of 3817?

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 3817 by each of the numbers from 1 to 3817 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)

3817 / 1 = 3817 (the remainder is 0, so 1 is a divisor of 3817)
3817 / 2 = 1908.5 (the remainder is 1, so 2 is not a divisor of 3817)
3817 / 3 = 1272.3333333333 (the remainder is 1, so 3 is not a divisor of 3817)
...
3817 / 3816 = 1.0002620545073 (the remainder is 1, so 3816 is not a divisor of 3817)
3817 / 3817 = 1 (the remainder is 0, so 3817 is a divisor of 3817)

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 3817 (i.e. 61.781874364574). 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 $\frac{N}{d} = D$ )

3817 / 1 = 3817 (the remainder is 0, so 1 and 3817 are divisors of 3817)
3817 / 2 = 1908.5 (the remainder is 1, so 2 is not a divisor of 3817)
3817 / 3 = 1272.3333333333 (the remainder is 1, so 3 is not a divisor of 3817)
...
3817 / 60 = 63.616666666667 (the remainder is 37, so 60 is not a divisor of 3817)
3817 / 61 = 62.573770491803 (the remainder is 35, so 61 is not a divisor of 3817)