What is the sum of the smallest prime and largest prime number less than 10? A. 7 B. 9 C. 10 D. 11 E. 12
Hint: Find the smallest and largest prime number between the numbers 1 to 10. Thus add both the values obtained.
Complete Step-by-Step solution: Prime numbers are the positive integers having only 2 factors that is 1 and itself. For example 6, its factors are 1, 2, 3 and 6, which has 4 factors in total. But if we are taking the number 11, the only factors are 1 and 11. Thus 11 is a prime number but 6 is not a prime number, it’s a composite number. We know that 1 is neither prime nor composite. Now let us write the prime numbers from 1 to 10. The prime numbers are = 2, 3, 5, 7. These are 4 prime numbers between the numbers 1 to 10. Out of these we can see that 2 is the smallest prime number and 7 is the largest prime number. \[\therefore \] The sum of smallest and largest prime number = 2 + 7 =9. \[\therefore \] We got the sum as 9. So option (b) is the correct answer.
Note: Every number greater than 1 can be divided by at least one prime number. All the prime numbers are odd, except for 2 which is the only even prime number. Each composite number can be factored into prime factors and individually all of these are unique in nature.