What are the divisors of 3703?

1, 7, 23, 161, 529, 3703

There is a total of 6 positive divisors.
The sum of these divisors is 4424.
The arithmetic mean is 737.33333333333.

6 odd divisors

1, 7, 23, 161, 529, 3703

How to compute the divisors of 3703?

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 3703 by each of the numbers from 1 to 3703 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)

3703 / 1 = 3703 (the remainder is 0, so 1 is a divisor of 3703)
3703 / 2 = 1851.5 (the remainder is 1, so 2 is not a divisor of 3703)
3703 / 3 = 1234.3333333333 (the remainder is 1, so 3 is not a divisor of 3703)
...
3703 / 3702 = 1.0002701242572 (the remainder is 1, so 3702 is not a divisor of 3703)
3703 / 3703 = 1 (the remainder is 0, so 3703 is a divisor of 3703)

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 3703 (i.e. 60.852280154486). 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 $\frac{N}{d} = D$ )

3703 / 1 = 3703 (the remainder is 0, so 1 and 3703 are divisors of 3703)
3703 / 2 = 1851.5 (the remainder is 1, so 2 is not a divisor of 3703)
3703 / 3 = 1234.3333333333 (the remainder is 1, so 3 is not a divisor of 3703)
...
3703 / 59 = 62.762711864407 (the remainder is 45, so 59 is not a divisor of 3703)
3703 / 60 = 61.716666666667 (the remainder is 43, so 60 is not a divisor of 3703)