What are the divisors of 3748?

1, 2, 4, 937, 1874, 3748

There is a total of 6 positive divisors.
The sum of these divisors is 6566.
The arithmetic mean is 1094.3333333333.

4 even divisors

2, 4, 1874, 3748

2 odd divisors

1, 937

How to compute the divisors of 3748?

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 3748 by each of the numbers from 1 to 3748 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)

3748 / 1 = 3748 (the remainder is 0, so 1 is a divisor of 3748)
3748 / 2 = 1874 (the remainder is 0, so 2 is a divisor of 3748)
3748 / 3 = 1249.3333333333 (the remainder is 1, so 3 is not a divisor of 3748)
...
3748 / 3747 = 1.0002668801708 (the remainder is 1, so 3747 is not a divisor of 3748)
3748 / 3748 = 1 (the remainder is 0, so 3748 is a divisor of 3748)

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 3748 (i.e. 61.220911460056). 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 $\frac{N}{d} = D$ )

3748 / 1 = 3748 (the remainder is 0, so 1 and 3748 are divisors of 3748)
3748 / 2 = 1874 (the remainder is 0, so 2 and 1874 are divisors of 3748)
3748 / 3 = 1249.3333333333 (the remainder is 1, so 3 is not a divisor of 3748)
...
3748 / 60 = 62.466666666667 (the remainder is 28, so 60 is not a divisor of 3748)
3748 / 61 = 61.44262295082 (the remainder is 27, so 61 is not a divisor of 3748)