Question

Explain whether $(3\times 12\times 101)+4$ is a prime number or a composite number.

Answer 1

Factorize to find whether $(3\times 12\times 101)+4$ factorizes into factors:

Given: $(3\times 12\times 101)+4$

$$\begin{gathered} (3\times 12\times 101)+4 \\ =(3\times 3\times 4\times 101)+4 \\ =4\left[3\times 3\times 101+1\right] \\ =4m \end{gathered}$$

Where $m=(3\times 3\times 101+1)$.

Now, since $(3\times 12\times 101)+4$can be factorized into two or more than two numbers so, $(3\times 12\times 101)+4$is not a prime number.

Hence, $(3\times 12\times 101)+4$ is a composite number.