What are the divisors of 3724?

1, 2, 4, 7, 14, 19, 28, 38, 49, 76, 98, 133, 196, 266, 532, 931, 1862, 3724

There is a total of 18 positive divisors.
The sum of these divisors is 7980.
The arithmetic mean is 443.33333333333.

12 even divisors

2, 4, 14, 28, 38, 76, 98, 196, 266, 532, 1862, 3724

6 odd divisors

1, 7, 19, 49, 133, 931

How to compute the divisors of 3724?

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 3724 by each of the numbers from 1 to 3724 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)

3724 / 1 = 3724 (the remainder is 0, so 1 is a divisor of 3724)
3724 / 2 = 1862 (the remainder is 0, so 2 is a divisor of 3724)
3724 / 3 = 1241.3333333333 (the remainder is 1, so 3 is not a divisor of 3724)
...
3724 / 3723 = 1.0002686005909 (the remainder is 1, so 3723 is not a divisor of 3724)
3724 / 3724 = 1 (the remainder is 0, so 3724 is a divisor of 3724)

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 3724 (i.e. 61.024585209569). 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 $\frac{N}{d} = D$ )

3724 / 1 = 3724 (the remainder is 0, so 1 and 3724 are divisors of 3724)
3724 / 2 = 1862 (the remainder is 0, so 2 and 1862 are divisors of 3724)
3724 / 3 = 1241.3333333333 (the remainder is 1, so 3 is not a divisor of 3724)
...
3724 / 60 = 62.066666666667 (the remainder is 4, so 60 is not a divisor of 3724)
3724 / 61 = 61.049180327869 (the remainder is 3, so 61 is not a divisor of 3724)