Question

Make a list of seven consecutive composite numbers less than 100 so that there is no prime number between them.

Answer 1

Hint: Here we have to find the seven consecutive composite numbers which is less than 100. Consecutive numbers are the numbers which occur one after the other. Composite numbers are defined as the number which has more than two factors i.e. factors along with one and the number itself. So we will find the group of numbers which are consecutive as well as composite numbers and also there is no prime number in between them.

Complete step by step solution:
We will first write all prime numbers between 1 and 100.
Prime numbers are:-
2, 3, 5, 7,
11, 13, 17, 19,
23, 29,
31, 37,
41, 43, 47,
53, 59,
61, 67,
71, 73, 79,
83, 89,
97
We can see that there is a huge gap between the prime numbers 89 and 97. That means consecutive numbers must lie between the prime numbers 89 and 97. We also know that numbers which are not prime numbers are called composite numbers.
Let us list all the numbers between 89 and 97. They are 90,91,92,93,94,95,96 and all of them are composite numbers.
Therefore, 7 consecutive composite numbers between less than 100 are 90, 91, 92, 93, 94, 95, and 96.

Note: To solve this question, we need to keep in mind the definitions of composite numbers and prime numbers. Prime number is defined as a number which has only two factors i.e. one and the number itself. All the numbers that are not prime numbers are known as composite numbers. 2 is the only prime number which is even. There are a total 24 prime numbers from 1 to 100. 4 is the smallest composite number and it is divisible by 1, 2 and 4. 1 is neither prime nor composite number.