What are the divisors of 3722?

1, 2, 1861, 3722

There is a total of 4 positive divisors.
The sum of these divisors is 5586.
The arithmetic mean is 1396.5.

2 even divisors

2, 3722

2 odd divisors

1, 1861

How to compute the divisors of 3722?

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 3722 by each of the numbers from 1 to 3722 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)

3722 / 1 = 3722 (the remainder is 0, so 1 is a divisor of 3722)
3722 / 2 = 1861 (the remainder is 0, so 2 is a divisor of 3722)
3722 / 3 = 1240.6666666667 (the remainder is 2, so 3 is not a divisor of 3722)
...
3722 / 3721 = 1.000268744961 (the remainder is 1, so 3721 is not a divisor of 3722)
3722 / 3722 = 1 (the remainder is 0, so 3722 is a divisor of 3722)

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 3722 (i.e. 61.008196170679). 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 $\frac{N}{d} = D$ )

3722 / 1 = 3722 (the remainder is 0, so 1 and 3722 are divisors of 3722)
3722 / 2 = 1861 (the remainder is 0, so 2 and 1861 are divisors of 3722)
3722 / 3 = 1240.6666666667 (the remainder is 2, so 3 is not a divisor of 3722)
...
3722 / 60 = 62.033333333333 (the remainder is 2, so 60 is not a divisor of 3722)
3722 / 61 = 61.016393442623 (the remainder is 1, so 61 is not a divisor of 3722)