What are the divisors of 3902?

1, 2, 1951, 3902

There is a total of 4 positive divisors.
The sum of these divisors is 5856.
The arithmetic mean is 1464.

2 even divisors

2, 3902

2 odd divisors

1, 1951

How to compute the divisors of 3902?

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 3902 by each of the numbers from 1 to 3902 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)

3902 / 1 = 3902 (the remainder is 0, so 1 is a divisor of 3902)
3902 / 2 = 1951 (the remainder is 0, so 2 is a divisor of 3902)
3902 / 3 = 1300.6666666667 (the remainder is 2, so 3 is not a divisor of 3902)
...
3902 / 3901 = 1.000256344527 (the remainder is 1, so 3901 is not a divisor of 3902)
3902 / 3902 = 1 (the remainder is 0, so 3902 is a divisor of 3902)

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 3902 (i.e. 62.465990746966). 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 $\frac{N}{d} = D$ )

3902 / 1 = 3902 (the remainder is 0, so 1 and 3902 are divisors of 3902)
3902 / 2 = 1951 (the remainder is 0, so 2 and 1951 are divisors of 3902)
3902 / 3 = 1300.6666666667 (the remainder is 2, so 3 is not a divisor of 3902)
...
3902 / 61 = 63.967213114754 (the remainder is 59, so 61 is not a divisor of 3902)
3902 / 62 = 62.935483870968 (the remainder is 58, so 62 is not a divisor of 3902)