Question

Write seven consecutive composite numbers less than 100.

Answer 1

Hint: Here, we will use the fact that the consecutive composite numbers are numbers other than prime numbers. So we will keep on subtracting the number with one as per asked in the question and checking if it is a prime number of consecutive numbers.


Complete step-by-step answer:
We are given that the number is 100.

We know that the consecutive numbers can be obtained by subtracting one to the number according to the question.

First, we will compute the first consecutive composite numbers before 100 by subtracting 1 from the obtained numbers.

\[ \Rightarrow 100 - 1 = 99\]
\[ \Rightarrow 99 - 1 = 98\]
\[ \Rightarrow 98 - 1 = 97\]

But since we know that 97 is a prime number, so we only be able to find two consecutive numbers before 100.

Now, we will skip 97 and find the other consecutive numbers.

\[ \Rightarrow 97 - 1 = 96\]
\[ \Rightarrow 96 - 1 = 95\]
\[ \Rightarrow 95 - 1 = 94\]
\[ \Rightarrow 94 - 1 = 93\]
\[ \Rightarrow 93 - 1 = 92\]
\[ \Rightarrow 92 - 1 = 91\]
\[ \Rightarrow 91 - 1 = 90\]

Since 90, 91, 92, 93, 94, 95, and 96 are seven consecutive numbers and all are composite.

Thus, the two consecutive composite numbers before are 90, 91, 92, 93, 94, 95 and 96.

Note: While solving these types of problems, the key concept is that we have to locate composite numbers in the top series, like from 90 onwards. We can’t find consecutive seven numbers from numbers 4 to 88. This is a really simple question, we just have to keep on subtracting by one until we get the seven composite numbers in row.