### When you multiply a prime and a composite number do you always get a composite number?

Product of a prime number and a composite number results in a composite number. Now consider the product of a composite number(a) and a prime number(b) is equal to c. i.e. c = a x b It is clear that c is divisible by both a and b. Also c is divisible by itself and 1, this means that c has more than two factors. A number having more than two factors is composite, therefore…