Question

What is the smallest composite number that has the five smallest prime numbers as factors?

Answer 1

Hint: Here first we need to understand the definition of prime numbers and composite numbers. Now, consider the first five numbers that have numbers that have only two factors, i.e. 1 and the number itself, and take their product. This product obtained will be our answer.

Complete step by step solution:
Here we have been asked to determine the smallest composite number that is divisible by the first five prime numbers. First we need to understand the definitions of prime and composite numbers.
(1) Prime numbers: - A prime number is a natural number that has only two factors, one factor is 1 and the other is the number itself. For example: - 2, 3, 5, 7 etc.
(2) Composite numbers: - A composite number is a natural number that has more than two factors. All the numbers which are not primes are composite in nature. For example: - 4, 6, 8, 9 etc.
Now, let us come to the question. To determine the smallest composite number that must have five smallest prime numbers as factors we must take the product of five smallest prime factors. Five smallest prime factors are: - 2, 3, 5, 7 and 11. Therefore, considering the product we get,
Required composite number = $2\times 3\times 5\times 7\times 11$
Required composite number = 2310
Hence, the required smallest composite number is 2310.

Note: You may note that 1 is neither a prime nor a composite number. Remember the definitions of some basic terms of elementary mathematics like whole numbers, natural numbers, rational and irrational numbers, integers etc. Note that there will be many composite numbers that will have 2, 3, 5, 7 and 11 as their factors but here we have to consider the smallest one.