What are the divisors of 3730?

1, 2, 5, 10, 373, 746, 1865, 3730

There is a total of 8 positive divisors.
The sum of these divisors is 6732.
The arithmetic mean is 841.5.

4 even divisors

2, 10, 746, 3730

4 odd divisors

1, 5, 373, 1865

How to compute the divisors of 3730?

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 3730 by each of the numbers from 1 to 3730 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)

3730 / 1 = 3730 (the remainder is 0, so 1 is a divisor of 3730)
3730 / 2 = 1865 (the remainder is 0, so 2 is a divisor of 3730)
3730 / 3 = 1243.3333333333 (the remainder is 1, so 3 is not a divisor of 3730)
...
3730 / 3729 = 1.0002681684098 (the remainder is 1, so 3729 is not a divisor of 3730)
3730 / 3730 = 1 (the remainder is 0, so 3730 is a divisor of 3730)

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 3730 (i.e. 61.07372593841). 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 $\frac{N}{d} = D$ )

3730 / 1 = 3730 (the remainder is 0, so 1 and 3730 are divisors of 3730)
3730 / 2 = 1865 (the remainder is 0, so 2 and 1865 are divisors of 3730)
3730 / 3 = 1243.3333333333 (the remainder is 1, so 3 is not a divisor of 3730)
...
3730 / 60 = 62.166666666667 (the remainder is 10, so 60 is not a divisor of 3730)
3730 / 61 = 61.147540983607 (the remainder is 9, so 61 is not a divisor of 3730)