What are the divisors of 3702?

1, 2, 3, 6, 617, 1234, 1851, 3702

There is a total of 8 positive divisors.
The sum of these divisors is 7416.
The arithmetic mean is 927.

4 even divisors

2, 6, 1234, 3702

4 odd divisors

1, 3, 617, 1851

How to compute the divisors of 3702?

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 3702 by each of the numbers from 1 to 3702 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)

3702 / 1 = 3702 (the remainder is 0, so 1 is a divisor of 3702)
3702 / 2 = 1851 (the remainder is 0, so 2 is a divisor of 3702)
3702 / 3 = 1234 (the remainder is 0, so 3 is a divisor of 3702)
...
3702 / 3701 = 1.000270197244 (the remainder is 1, so 3701 is not a divisor of 3702)
3702 / 3702 = 1 (the remainder is 0, so 3702 is a divisor of 3702)

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 3702 (i.e. 60.844062980705). 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 $\frac{N}{d} = D$ )

3702 / 1 = 3702 (the remainder is 0, so 1 and 3702 are divisors of 3702)
3702 / 2 = 1851 (the remainder is 0, so 2 and 1851 are divisors of 3702)
3702 / 3 = 1234 (the remainder is 0, so 3 and 1234 are divisors of 3702)
...
3702 / 59 = 62.745762711864 (the remainder is 44, so 59 is not a divisor of 3702)
3702 / 60 = 61.7 (the remainder is 42, so 60 is not a divisor of 3702)