What are the divisors of 1946?

1, 2, 7, 14, 139, 278, 973, 1946

There is a total of 8 positive divisors.
The sum of these divisors is 3360.
The arithmetic mean is 420.

4 even divisors

2, 14, 278, 1946

4 odd divisors

1, 7, 139, 973

How to compute the divisors of 1946?

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 1946 by each of the numbers from 1 to 1946 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)

1946 / 1 = 1946 (the remainder is 0, so 1 is a divisor of 1946)
1946 / 2 = 973 (the remainder is 0, so 2 is a divisor of 1946)
1946 / 3 = 648.66666666667 (the remainder is 2, so 3 is not a divisor of 1946)
...
1946 / 1945 = 1.0005141388175 (the remainder is 1, so 1945 is not a divisor of 1946)
1946 / 1946 = 1 (the remainder is 0, so 1946 is a divisor of 1946)

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 1946 (i.e. 44.113490000226). 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 $\frac{N}{d} = D$ )

1946 / 1 = 1946 (the remainder is 0, so 1 and 1946 are divisors of 1946)
1946 / 2 = 973 (the remainder is 0, so 2 and 973 are divisors of 1946)
1946 / 3 = 648.66666666667 (the remainder is 2, so 3 is not a divisor of 1946)
...
1946 / 43 = 45.255813953488 (the remainder is 11, so 43 is not a divisor of 1946)
1946 / 44 = 44.227272727273 (the remainder is 10, so 44 is not a divisor of 1946)