Question

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

Answer 1

Hint: First we have to know that composite numbers are the natural numbers (Counting numbers) which are not prime [ numbers which have only two factors (1 and itself)] and have more than two factors. It means each composite number written as the product of two or more numbers. Hence the number which has more than two factors is a composite.

Complete step-by-step solution:
The natural numbers (positive integers) lie between \[1\] and \[10\] are \[2,3,4,5,6,7,8,9\].
The positive integers (natural numbers) \[2,3,5,7\] are prime numbers because they can be divided by only two factors, one and itself. Hence \[2,3,5,7\] are not composite numbers.
But the remaining numbers \[4,6,8,9\] have more than two factors. The divisors of \[4\] are \[1,2,4\]. The divisors of \[6\] are \[1,2,3,6\], and so for \[8,9\]. Hence those numbers satisfy the condition of a composite number as mentioned above.
Hence the numbers \[4,6,8,9\] are composite numbers between \[1\] and \[10\].

Additional information: Composite numbers are divided into two main types of composite numbers, namely odd composite numbers and even composite numbers. All the odd integers which are not prime are odd composite numbers and those numbers have the odd divisors and satisfy the composite condition. All the even integers which are not prime are even composite numbers and those numbers satisfy the composite condition.

Note: Any even number which is greater than 2 is a composite number. \[4\]is the smallest (even) composite number and \[9\] is the smallest odd composite number. Also note that zero (\[0\]) is neither prime nor a composite number because it does not have any factors.