What are the divisors of 3753?

1, 3, 9, 27, 139, 417, 1251, 3753

There is a total of 8 positive divisors.
The sum of these divisors is 5600.
The arithmetic mean is 700.

8 odd divisors

1, 3, 9, 27, 139, 417, 1251, 3753

How to compute the divisors of 3753?

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 3753 by each of the numbers from 1 to 3753 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)

3753 / 1 = 3753 (the remainder is 0, so 1 is a divisor of 3753)
3753 / 2 = 1876.5 (the remainder is 1, so 2 is not a divisor of 3753)
3753 / 3 = 1251 (the remainder is 0, so 3 is a divisor of 3753)
...
3753 / 3752 = 1.0002665245203 (the remainder is 1, so 3752 is not a divisor of 3753)
3753 / 3753 = 1 (the remainder is 0, so 3753 is a divisor of 3753)

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 3753 (i.e. 61.261733569986). 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 $\frac{N}{d} = D$ )

3753 / 1 = 3753 (the remainder is 0, so 1 and 3753 are divisors of 3753)
3753 / 2 = 1876.5 (the remainder is 1, so 2 is not a divisor of 3753)
3753 / 3 = 1251 (the remainder is 0, so 3 and 1251 are divisors of 3753)
...
3753 / 60 = 62.55 (the remainder is 33, so 60 is not a divisor of 3753)
3753 / 61 = 61.524590163934 (the remainder is 32, so 61 is not a divisor of 3753)