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Mathematics Activity :
Composite Numbers and Prime Numbers

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1. How many prime numbers are there between 1 and 10?
Answer: 4
There are 4 prime numbers between 1 and 10. They are 2, 3, 5, and 7.


2. How many prime numbers are there up to 20?
Answer: 8
There are 8 prime numbers up to 20. They are 2, 3, 5, 7, 11, 13, 17, and 19.


3. What is the sum of the prime numbers between 20 and 30?
Answer: 3
The prime numbers between 20 and 30 are 23 and 29. Their sum is 52.



4. How many prime numbers are there from 30 to 50?
Answer: 5
There are 5 prime numbers from 30 to 50. They are 31, 37, 41, 43, and 47.


5. Which of the following is a composite number: 37, 47, 57, 67?
Answer: 57
37, 47 and 67 are prime numbers. 57 is a composite number because it has more than two factors (1, 3, 19, 57).


6. How many composite numbers are there from 61 to 79?
Answer: 14
There are 14 composite numbers from 61 to 79. They are 62, 63, 64, 65, 66, 68, 69, 70, 72, 74, 75, 76, 77, and 78.


7. Which is the prime number between 90 and 100?
Answer: 97
97 is the only prime number between 90 and 100.


8. How many prime numbers are there up to 50?
Answer: 15
There are 15 prime numbers up to 50. They are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, and 47.


9. How many prime numbers are there between 50 and 100?
Answer: 10
There are 10 prime numbers between 50 and 100. They are 53, 59, 61, 67, 71, 73, 79, 83, 89, and 97.


10. How many even prime numbers between 1 and 50?
Answer: 1
There is only one even prime number and that is 2.


11. How many pairs of prime numbers are there to express 18 as the sum of two prime numbers?
Answer: 2
Two pairs of prime numbers exist: 5 + 13 = 18 and 7 + 11 = 18.


12. How many pairs of prime numbers are there to express 20 as the sum of two prime numbers?
Answer: 2
Two pairs of prime numbers exist: 3 + 17 = 20 and 7 + 13 = 20.


13. How many pairs of prime numbers are there to express 24 as the sum of two prime numbers?
Answer: 3
Three pairs of prime numbers exist: 5 + 19 = 24, 7 + 17 = 24, 11 + 13 = 24.


14. What is the sum of the prime numbers coming immediately before and after 71?
Answer: 140
The prime numbers immediately before and after 71 are 67 and 73. Their sum is 140.


15. What is the sum of the prime numbers coming immediately before and after 50?
Answer: 100
The prime numbers immediately before and after 50 are 47 and 53. Their sum is 100.


16. What is the difference between the greatest and the smallest prime numbers coming in between 20 and 40?
Answer: 14
The greatest and smallest prime numbers between 20 and 40 are 37 and 23. Their difference is 14.


17. What is the difference between the fifth and the second prime numbers coming after 7?
Answer: 10
The fifth and second prime numbers after 7 are 23 and 13. Their difference is 10.


18. What is the smallest composite number?
Answer: 4
1 is neither a prime number nor a composite number because it has only one factor. 2 and 3 are prime numbers because each has only two factors. Thus 4 is the smallest composite number.


19. 11 is a prime factor of 187. What is the other prime factor?
Answer: 17
Note that 11 X 17 = 187. The answer is obtained by dividing 187 by 11.


20. 7 is a prime factor of 133. What is the other prime factor?
Answer: 19
Note that 7 X 19 = 133. The answer is obtained by dividing 133 by 7.


21. Two prime numbers whose difference is 2 are called twin prime numbers, e.g., 3 and 5. How many twin prime numbers are there upto 50?
Answer: 5
The 5 twin prime numbers upto 50 are: 3 and 5; 5 and 7; 11 and 13; 17 and 19; 29 and 31; 41 and 43.


22. Two prime numbers whose difference is 2 are called twin prime numbers, e.g., 3 and 5. How many twin prime numbers are there between 50 and 100?
Answer: 2
The 2 twin prime numbers between 50 and 100 are: 59 and 61; 71 and 73.


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