### Divisors of a number - example II

What are the divisors of \(35\)?

\(35:1=35\) (remainder \(0\)) \(\rightarrow\) hence \(1\) and \(35\) are divisors of \(35\)

\(35:2=17\) (remainder \(1\)) \(\rightarrow\) hence \(2\) is not a divisor
of \(35\)

\(35:3=11\) (remainder \(2\)) \(\rightarrow\) hence \(3\) is not a divisor
of \(35\)

\(35:4=8\) (remainder \(3\)) \(\rightarrow\) hence \(4\) is not a divisor
of \(35\)

\(35:5=7\) (remainder \(0\)) \(\rightarrow\) hence \(5\) and \(7\) are divisors of \(35\)

\(35:6=5\) (remainder \(5\)) \(\rightarrow\) hence \(6\) is not a divisor
of \(35\)

Similarly as in example I, we may conclude that the divisors of \(35\) are **precisely**
the following ones: \[D_{35} = \{1, 5, 7, 35\}.\]

Is it really necessary to make all those computations to determine the divisors of \(35\)? Not really, if we take into account that if a number is not divisible by \(2\), then it is also not divisible by any multiple of \(2\).

Thus, we do not need to check whether \(35\) is divisible by \(4\) or by \(6\), since we already know that it is not divisible by \(2\).