What are the divisors of 3754?

1, 2, 1877, 3754

There is a total of 4 positive divisors.
The sum of these divisors is 5634.
The arithmetic mean is 1408.5.

2 even divisors

2, 3754

2 odd divisors

1, 1877

How to compute the divisors of 3754?

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 3754 by each of the numbers from 1 to 3754 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)

3754 / 1 = 3754 (the remainder is 0, so 1 is a divisor of 3754)
3754 / 2 = 1877 (the remainder is 0, so 2 is a divisor of 3754)
3754 / 3 = 1251.3333333333 (the remainder is 1, so 3 is not a divisor of 3754)
...
3754 / 3753 = 1.0002664535039 (the remainder is 1, so 3753 is not a divisor of 3754)
3754 / 3754 = 1 (the remainder is 0, so 3754 is a divisor of 3754)

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 3754 (i.e. 61.269894728162). 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 $\frac{N}{d} = D$ )

3754 / 1 = 3754 (the remainder is 0, so 1 and 3754 are divisors of 3754)
3754 / 2 = 1877 (the remainder is 0, so 2 and 1877 are divisors of 3754)
3754 / 3 = 1251.3333333333 (the remainder is 1, so 3 is not a divisor of 3754)
...
3754 / 60 = 62.566666666667 (the remainder is 34, so 60 is not a divisor of 3754)
3754 / 61 = 61.540983606557 (the remainder is 33, so 61 is not a divisor of 3754)