Solutions to Questions on Prime and Composite Numbers

Detailed solutions with full explanations to questions on prime and composite numbers are presented.

1. 
   Which of the following numbers are prime?
   1, 6.3, 11, 14, 13, 21, 23, 4/5, 100, 123.
   Solution
   The following are prime numbers.
   11, 13, 23: each of these is divisible by 1 and itself only.
   The following are NOT prime numbers.
   1 : not greater than 1
   6.3: decimal number
   14: divisible by 1, itself, 2, 7
   21: divisible by 1, itself, 3, 7
   4/5 : not a whole number
   100: divisible by 1, itself, 2, 4, 5, 10,...
   123: divisible by 1, itself, 3, 41.
2. 
   Which of the following numbers are composite?
   1, 8.4, 15, 13, 9/2, 24, 33.
   Solution
   The following are composite numbers.
   15: divisible by 1, itself, 5, 3.
   24: divisible by 1, itself, 3, 4, 6, 8, 12.
   33: divisible by 1, itself, 3, 11.
   The following are NOT composite numbers.
   1 : not greater than 1
   8.4: decimal number
   13: prime number, divisible by 1 and itself only.
   9/2: not whole number
3. 
   List all prime numbers between 30 and 50 inclusive.
   Solution
   Prime numbers between 30 and 50 are.
   31, 37, 41, 43, 47
4. 
   List all composite numbers between 100 and 110 inclusive.
   Solution
   Composite numbers between 100 and 110 inclusive are.
   100, 102, 104, 105, 106, 108, 110
5. 
   Is the sum of two prime numbers always a prime number?
   Solution
   No. Here is an example.
   3 + 7 = 10 , 3 and 7 are prime numbers but not their sum 10.
6. 
   Is the product of two prime numbers also a prime number?
   Solution
   Never because it will have 1 and itself as factors and also the two numbers involved in the product.
   Example: 7 × 11 = 77 ,77 has 1, itself, 7 and 11 as factors.
7. 
   Which is the largest 3 digit prime number?
   Solution
   Start with the largest three digit number 999.
   999 is not a prime number
   998 is not a prime number
   Answer: 997 a prime number
8. 
   Which is the smallest 2 digit prime number?
   Solution
   Start with the smallest 2 digit number 10.
   10 is not a prime number
   Answer: 11 is a prime number
9. 
   List all the two digit prime numbers that can be made from the digits 1, 3 and 6 (used only once each).
   Solution
   13, 31 and 61
10. 
    Can you find a prime number whose least significant digit (digit on the right) is 0?
    Solution
    No because any number with 0 as the least significant digit is divisible by 1, itself and at least 2, 5 and 10.
11. 
    Can you find a two digit prime number whose least significant digit (digit on the right) is 5? Solution
    No because any two digit number with 5 as the least significant digit is divisible by 1, itself and at least 5.
12. 
    Can you find a prime number such that the sum of all its digits is equal to 12?
    No because any number whose digits adds up to 12 is divisible at least by 1, itself and 3 (because 12 is divisible by 3).

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