What are the divisors of 3673?

1, 3673

There is a total of 2 positive divisors.
The sum of these divisors is 3674.
The arithmetic mean is 1837.

2 odd divisors

1, 3673

How to compute the divisors of 3673?

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 3673 by each of the numbers from 1 to 3673 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)

3673 / 1 = 3673 (the remainder is 0, so 1 is a divisor of 3673)
3673 / 2 = 1836.5 (the remainder is 1, so 2 is not a divisor of 3673)
3673 / 3 = 1224.3333333333 (the remainder is 1, so 3 is not a divisor of 3673)
...
3673 / 3672 = 1.0002723311547 (the remainder is 1, so 3672 is not a divisor of 3673)
3673 / 3673 = 1 (the remainder is 0, so 3673 is a divisor of 3673)

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 3673 (i.e. 60.605280298007). 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 $\frac{N}{d} = D$ )

3673 / 1 = 3673 (the remainder is 0, so 1 and 3673 are divisors of 3673)
3673 / 2 = 1836.5 (the remainder is 1, so 2 is not a divisor of 3673)
3673 / 3 = 1224.3333333333 (the remainder is 1, so 3 is not a divisor of 3673)
...
3673 / 59 = 62.254237288136 (the remainder is 15, so 59 is not a divisor of 3673)
3673 / 60 = 61.216666666667 (the remainder is 13, so 60 is not a divisor of 3673)