What are the divisors of 3898?

1, 2, 1949, 3898

There is a total of 4 positive divisors.
The sum of these divisors is 5850.
The arithmetic mean is 1462.5.

2 even divisors

2, 3898

2 odd divisors

1, 1949

How to compute the divisors of 3898?

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 3898 by each of the numbers from 1 to 3898 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)

3898 / 1 = 3898 (the remainder is 0, so 1 is a divisor of 3898)
3898 / 2 = 1949 (the remainder is 0, so 2 is a divisor of 3898)
3898 / 3 = 1299.3333333333 (the remainder is 1, so 3 is not a divisor of 3898)
...
3898 / 3897 = 1.0002566076469 (the remainder is 1, so 3897 is not a divisor of 3898)
3898 / 3898 = 1 (the remainder is 0, so 3898 is a divisor of 3898)

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 3898 (i.e. 62.433965115152). 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 $\frac{N}{d} = D$ )

3898 / 1 = 3898 (the remainder is 0, so 1 and 3898 are divisors of 3898)
3898 / 2 = 1949 (the remainder is 0, so 2 and 1949 are divisors of 3898)
3898 / 3 = 1299.3333333333 (the remainder is 1, so 3 is not a divisor of 3898)
...
3898 / 61 = 63.901639344262 (the remainder is 55, so 61 is not a divisor of 3898)
3898 / 62 = 62.870967741935 (the remainder is 54, so 62 is not a divisor of 3898)