What are the divisors of 1898?

1, 2, 13, 26, 73, 146, 949, 1898

There is a total of 8 positive divisors.
The sum of these divisors is 3108.
The arithmetic mean is 388.5.

4 even divisors

2, 26, 146, 1898

4 odd divisors

1, 13, 73, 949

How to compute the divisors of 1898?

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 1898 by each of the numbers from 1 to 1898 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)

1898 / 1 = 1898 (the remainder is 0, so 1 is a divisor of 1898)
1898 / 2 = 949 (the remainder is 0, so 2 is a divisor of 1898)
1898 / 3 = 632.66666666667 (the remainder is 2, so 3 is not a divisor of 1898)
...
1898 / 1897 = 1.0005271481286 (the remainder is 1, so 1897 is not a divisor of 1898)
1898 / 1898 = 1 (the remainder is 0, so 1898 is a divisor of 1898)

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 1898 (i.e. 43.566041821584). 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 $\frac{N}{d} = D$ )

1898 / 1 = 1898 (the remainder is 0, so 1 and 1898 are divisors of 1898)
1898 / 2 = 949 (the remainder is 0, so 2 and 949 are divisors of 1898)
1898 / 3 = 632.66666666667 (the remainder is 2, so 3 is not a divisor of 1898)
...
1898 / 42 = 45.190476190476 (the remainder is 8, so 42 is not a divisor of 1898)
1898 / 43 = 44.139534883721 (the remainder is 6, so 43 is not a divisor of 1898)