Write seven consecutive composite numbers less than $100$ so that there is no prime number between them.
Last updated date: 27th Mar 2023
•
Total views: 310.5k
•
Views today: 4.90k
Answer
310.5k+ views
Hint- This question can be solved by writing all composite numbers on the higher side i.e. from $90$ onwards.
In order to write seven consecutive composite numbers between $1$ and $100$ we have to consider the numbers of the higher side in counting because if we take smaller numbers there is more probability of prime numbers.
For example: If we start from first prime number i.e.
$2$ and $3$ are prime numbers followed by $5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97$.
When we see these numbers we get, composite numbers
$
4,6,8,9,10,12,14,15,16,18,20,22,24,25,26,27,28,30,32,33,34,35,36,38,39,40,42,44,45,46,48,49,50, \\
51,52,54,55,56,57,58,60,62,63,64,65,66,68,69,70,72,74,75,76,77,78,80,81,82,84,85,86,87,88,90, \\
91,92,93,94,95,96,98,99. \\
$
On seeing these numbers we find that we are not able to get $5$ consecutive composite numbers from $4$ to $88$ . And when we start from $90$ to $96$ we get seven consecutive composite numbers.
Note- Whenever we face such types of questions the key concept is that we have to locate composite numbers in the top series i.e. $90$ onwards . Like we did in this question. We can’t find consecutive seven composite numbers from $4$ to $88$.
In order to write seven consecutive composite numbers between $1$ and $100$ we have to consider the numbers of the higher side in counting because if we take smaller numbers there is more probability of prime numbers.
For example: If we start from first prime number i.e.
$2$ and $3$ are prime numbers followed by $5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97$.
When we see these numbers we get, composite numbers
$
4,6,8,9,10,12,14,15,16,18,20,22,24,25,26,27,28,30,32,33,34,35,36,38,39,40,42,44,45,46,48,49,50, \\
51,52,54,55,56,57,58,60,62,63,64,65,66,68,69,70,72,74,75,76,77,78,80,81,82,84,85,86,87,88,90, \\
91,92,93,94,95,96,98,99. \\
$
On seeing these numbers we find that we are not able to get $5$ consecutive composite numbers from $4$ to $88$ . And when we start from $90$ to $96$ we get seven consecutive composite numbers.
Note- Whenever we face such types of questions the key concept is that we have to locate composite numbers in the top series i.e. $90$ onwards . Like we did in this question. We can’t find consecutive seven composite numbers from $4$ to $88$.
Recently Updated Pages
If ab and c are unit vectors then left ab2 right+bc2+ca2 class 12 maths JEE_Main

A rod AB of length 4 units moves horizontally when class 11 maths JEE_Main

Evaluate the value of intlimits0pi cos 3xdx A 0 B 1 class 12 maths JEE_Main

Which of the following is correct 1 nleft S cup T right class 10 maths JEE_Main

What is the area of the triangle with vertices Aleft class 11 maths JEE_Main

The coordinates of the points A and B are a0 and a0 class 11 maths JEE_Main

Trending doubts
What was the capital of Kanishka A Mathura B Purushapura class 7 social studies CBSE

Difference Between Plant Cell and Animal Cell

Write an application to the principal requesting five class 10 english CBSE

Ray optics is valid when characteristic dimensions class 12 physics CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Tropic of Cancer passes through how many states? Name them.

Write the 6 fundamental rights of India and explain in detail

Write a letter to the principal requesting him to grant class 10 english CBSE

Name the Largest and the Smallest Cell in the Human Body ?
