Question

Is 43 a prime number?

Answer 1

Hint: From the question we have been asked to find whether the number \[43\] is prime number or not. For this question we will take the help of the definition of prime number and also we will take the help of some examples and see whether the given number is a prime number or not.

Complete step-by-step solution:
A prime number is one that has its factors only itself and one.
So, for instance \[3\] is a prime number and \[4\]is not:
\[\Rightarrow 1\times 3=3\] and that’s all we can get for three so three is the prime number.
\[\Rightarrow 1\times 4=2\times 2=4\] four has two sets of factors and therefore it is not a prime number.
So, we will see if there are any factors for \[43\] other than \[\Rightarrow 1\times 43\].
Now, we will try and multiply numbers and get \[43\].
The number \[43\] is odd so nothing times \[2\] will work.
\[\Rightarrow 4+3=7\] which is not divisible by three, so nothing times \[3\] will work.
 The number \[43\] does not end with \[0\] or \[5\], so it is not divisible by \[5\].
\[\Rightarrow 7\times 6=42\] close to the number but not the number. So, nothing seven will work.
Finally we will check for times two,
\[\Rightarrow 23\times 2=46\]
And there is no sense in continuing as if two times twenty three is too big, nothing beyond this point will be smaller.
Therefore, \[43\] is not a prime number.

Note: students should have good knowledge in the concept of prime numbers and must have good knowledge in the application part of its definition. In fact we would have stopped much earlier because we already know that anything times \[2,3,4,5...\] wouldn’t work.