What are the divisors of 3749?

1, 23, 163, 3749

There is a total of 4 positive divisors.
The sum of these divisors is 3936.
The arithmetic mean is 984.

4 odd divisors

1, 23, 163, 3749

How to compute the divisors of 3749?

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 3749 by each of the numbers from 1 to 3749 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)

3749 / 1 = 3749 (the remainder is 0, so 1 is a divisor of 3749)
3749 / 2 = 1874.5 (the remainder is 1, so 2 is not a divisor of 3749)
3749 / 3 = 1249.6666666667 (the remainder is 2, so 3 is not a divisor of 3749)
...
3749 / 3748 = 1.0002668089648 (the remainder is 1, so 3748 is not a divisor of 3749)
3749 / 3749 = 1 (the remainder is 0, so 3749 is a divisor of 3749)

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 3749 (i.e. 61.229078059367). 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 $\frac{N}{d} = D$ )

3749 / 1 = 3749 (the remainder is 0, so 1 and 3749 are divisors of 3749)
3749 / 2 = 1874.5 (the remainder is 1, so 2 is not a divisor of 3749)
3749 / 3 = 1249.6666666667 (the remainder is 2, so 3 is not a divisor of 3749)
...
3749 / 60 = 62.483333333333 (the remainder is 29, so 60 is not a divisor of 3749)
3749 / 61 = 61.459016393443 (the remainder is 28, so 61 is not a divisor of 3749)