What are the divisors of 3746?

1, 2, 1873, 3746

There is a total of 4 positive divisors.
The sum of these divisors is 5622.
The arithmetic mean is 1405.5.

2 even divisors

2, 3746

2 odd divisors

1, 1873

How to compute the divisors of 3746?

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 3746 by each of the numbers from 1 to 3746 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)

3746 / 1 = 3746 (the remainder is 0, so 1 is a divisor of 3746)
3746 / 2 = 1873 (the remainder is 0, so 2 is a divisor of 3746)
3746 / 3 = 1248.6666666667 (the remainder is 2, so 3 is not a divisor of 3746)
...
3746 / 3745 = 1.0002670226969 (the remainder is 1, so 3745 is not a divisor of 3746)
3746 / 3746 = 1 (the remainder is 0, so 3746 is a divisor of 3746)

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 3746 (i.e. 61.204574992397). 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 $\frac{N}{d} = D$ )

3746 / 1 = 3746 (the remainder is 0, so 1 and 3746 are divisors of 3746)
3746 / 2 = 1873 (the remainder is 0, so 2 and 1873 are divisors of 3746)
3746 / 3 = 1248.6666666667 (the remainder is 2, so 3 is not a divisor of 3746)
...
3746 / 60 = 62.433333333333 (the remainder is 26, so 60 is not a divisor of 3746)
3746 / 61 = 61.409836065574 (the remainder is 25, so 61 is not a divisor of 3746)