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Question Identify whether each statement is true or false. Explain.
(a) There is no prime number whose unit digit is 4.
(b) A product of primes can also be prime.
(c) Prime numbers do not have any factors.
(d) All even numbers are composite numbers.
(e) 2 is a prime and so is the next number, 3. For every other prime, the next number is composite.
(a) True – The reason is that if the unit digit is 4 the number will become an even number.
(b) False – A product of primes can’t be prime because the product of primes is also divisible by the numbers itself.
(c) False – They also have two factors i.e., 1 and number itself.
(d) False – 2 has two factors 1 and 2, so except 2 all even numbers are composite.
(e) True – Except 2, for every prime number the next number is composite.