Question 9 - Figure it out - Page 114, 115 - Chapter 5 Class 6 - Prime Time (Ganita Prakash)

Transcript

Question 9 (a) Identify whether each statement is true or false. Explain. a. There is no prime number whose units digit is 4. Any number ending in 4 is an even number and divisible by 2, so it cannot be prime ∴ Statement is true Question 9 (b) Identify whether each statement is true or false. Explain. b. A product of primes can also be prime. The product of two or more prime numbers will always be a composite number because its factors will include the primes that were multiplied together. Example: 2 × 3 = 6 has factors 1, 2, 3, 6 So, 6 is prime ∴ Statement is false Question 9 (c) Identify whether each statement is true or false. Explain. c. Prime numbers do not have any factors. Prime numbers are those numbers which have only 2 factors So, Prime number have 2 factors ∴ Statement is false Question 9 (d) Identify whether each statement is true or false. Explain. d. All even numbers are composite numbers. 2 is an even number And it is prime So, all even numbers are not composite ∴ Statement is false Question 9 (e) Identify whether each statement is true or false. Explain. e. 2 is a prime and so is the next number, 3. For every other prime, the next number is composite.Let’s look at all prime numbers till 100 We notice that Every prime number other than 2 is an odd number. The next consecutive number will always be an even number greater than 2, which must be composite. ∴ Statement is true