What are the divisors of 3743?

1, 19, 197, 3743

There is a total of 4 positive divisors.
The sum of these divisors is 3960.
The arithmetic mean is 990.

4 odd divisors

1, 19, 197, 3743

How to compute the divisors of 3743?

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 3743 by each of the numbers from 1 to 3743 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)

3743 / 1 = 3743 (the remainder is 0, so 1 is a divisor of 3743)
3743 / 2 = 1871.5 (the remainder is 1, so 2 is not a divisor of 3743)
3743 / 3 = 1247.6666666667 (the remainder is 2, so 3 is not a divisor of 3743)
...
3743 / 3742 = 1.0002672367718 (the remainder is 1, so 3742 is not a divisor of 3743)
3743 / 3743 = 1 (the remainder is 0, so 3743 is a divisor of 3743)

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 3743 (i.e. 61.18006211177). 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 $\frac{N}{d} = D$ )

3743 / 1 = 3743 (the remainder is 0, so 1 and 3743 are divisors of 3743)
3743 / 2 = 1871.5 (the remainder is 1, so 2 is not a divisor of 3743)
3743 / 3 = 1247.6666666667 (the remainder is 2, so 3 is not a divisor of 3743)
...
3743 / 60 = 62.383333333333 (the remainder is 23, so 60 is not a divisor of 3743)
3743 / 61 = 61.360655737705 (the remainder is 22, so 61 is not a divisor of 3743)