Question

Write down separately the prime and composite numbers less than 20.

Answer 1

Hint: In this question, we need to look into the basic definitions of the number system. Then from the definition of prime numbers and composite numbers we can list the prime and composite numbers that are less than 20.

Complete step-by-step solution -
Let us first look at some of the basic definitions.
NUMBER: A number tells us how many times a unit is contained in a given quantity.
NUMERAL: A group of figures or digits, representing a number is called a numeral.
Types of number system:
Binary number system
Octal number system
Hexadecimal number system
Roman number system
Decimal number system
DECIMAL NUMBER SYSTEM: Numeric values are represented by using digits from 0 to 9.
Again numbers in the decimal system are classified as real numbers.
Real numbers are classified into rational numbers and irrational numbers.
Rational numbers are again classified into integer and non-integer rational numbers.
Again integers are classified into:

Whole number

Positive integer

Negative integer

Natural number

The decimal number system is the standard system for denoting integer and non-integer numbers.
NATURAL NUMBERS: Numbers starting from 1, having no fraction part, which we use in counting the objects, denoted by N.
\[N=\left\{ 1,2,3...... \right\}\]
WHOLE NUMBERS: The system of Natural numbers along with number 0, is called whole number and is denoted by W.
\[W=\left\{ 0,1,2,3...... \right\}\]
Different Types of Natural Number:
EVEN NUMBER: A number, which is multiple of 2 is called an even number.
ODD NUMBER: A number, which is not multiple of 2 is called an odd number.
PRIME NUMBER: The number which can be divided only by itself and 1 is called prime number.
COMPOSITE NUMBER: The number which can be divided by a number other than 1 and the number itself is called composite number.
CONSECUTIVE NUMBER: A series of numbers in which each number is greater by 1 than the number which precedes it.
Now, let us list the prime numbers less than 20:
2, 3, 5, 7, 11, 13, 17, 19.
List of composite numbers that are less than 20:
4, 6, 8, 10, 12, 16, 18.

Note: It is important to note that composite numbers less than 20 are the numbers which are not prime and 1 that are less than 20. It means that the numbers which can be divided by numbers other than 1 and itself.
For example the number 12 can be divided by 2 , divided by 3 , divided by 6 and also divided by 1 and 12. Hence, 12 is a composite number.
Whereas, when we consider 7 it is divided by 1 and is divided by 7 but not any other number. Hence, 7 is a prime number.