Which of the following numbers is the product of exactly three distinct prime numbers : 45, 60, 91, 105, 330? Class 6

Which of the following numbers is the product of exactly three distinct prime numbers : 45, 60, 91, 105, 330? Class 6

Question 1.

Which of the following numbers is the product of exactly three distinct prime numbers : 45, 60, 91, 105, 330? Class 6

Solution:

105, because 105 = 3 × 5 × 7.

Question 2.

How many three-digit prime numbers can you make using each of 2, 4 and 5 once? Class 6

Solution:

No such number can be made, because in every such three digit number, unit digit will be either 2 or 4 or 5. If unit digit is 2 or 4, it will have a factor 2 and if the unit digit is 5, it will have a factor 5.

Question 3.

Observe that 3 is a prime number, and 2 × 3 + 1 = 7is also a prime. Are there other primes for which doubling and adding 1 gives another prime? Find at least five such examples. Class 6

Solution:

Such numbers may be: 2 × 5 + 1 = 11, 2 × 2 + 1 = 5, 2 × 23 + 1 = 47, 2 × 29 + 1 = 59. 2 × 41 + 1 = 83.