Question

What is a composite number between \[1\] and \[10\]?

Answer 1

Hint: We are asked to find the composite number between \[1\] and \[10\]. Composite numbers are those numbers which have the factors other than one and the number itself. The best and the easy way to find out if a number is composite or not is by performing the divisibility tests upon the numbers. The divisibility tests to be performed are \[2,3,5,7,11\] and \[13\].

Complete step by step solution:
Now let us have a brief regarding the composite numbers. Whole numbers that are not prime numbers are called composite numbers as they are divisible by two or more numbers. All even numbers except \[2\] are composite numbers. \[1\] is neither prime nor composite. \[4\] is the smallest composite number.
Now let us find out the composite numbers between \[1\] and \[10\].
As we know that \[1\] is neither prime nor composite, we will be omitting \[1\]. Also, \[2\] is the only even prime number, so \[2\] will also be omitted from the list.
Now let us consider \[3\], the factors that are associated with \[3\] are \[1,3\]. We can observe that it has only two factors too \[1\]and number itself, so it is a prime number.
On considering \[4\], the factors of \[4\] are \[1,2,4\]. We can observe that it has more than two factors. Hence, it is a composite number.
Let us consider \[5\], the factors of \[5\] are\[1,5\]. We can observe that it has only two factors. Hence, it is a prime number.
On considering \[6\], the factors of \[6\] are \[1,2,3,6\]. We observe that it has more than two factors other than one and the number itself, hence \[6\] is a composite number.
Let us consider \[7\]now, the factors of \[7\] are \[1,7\]. Therefore, \[7\] is a prime number.
On considering\[8\], the factors of \[8\]are\[1,2,4,8\]. Since it has four factors, it is a composite number.
On considering \[9\], the factors of \[9\] are \[1,3,9\]. Hence \[9\] is a composite number.
Since we are asked to find the composite numbers between \[1\] and \[10\], we would not be considering \[1\] and \[10\].

\[\therefore \] The composite numbers between \[1\] and \[10\] are \[4,6,8,9\].

Note: The composite numbers with two prime factors are called semi prime or \[2\]-almost prime. Composite numbers are also called rectangular numbers because they can be expressed as a product of two integers.