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Is 2 a Prime Number? The question often arises and is confusing due to the unique nature of the number 2. 2 is a prime number. Prime Numbers are defined as natural numbers that are divisible by only 1 and the number itself. Thus, a number that has exactly two factors is called a prime number. The number 2 has exactly two factors 1 and itself which makes number 2 a prime number. 2 is also a unique prime number as it is the only even prime number.
Prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, etc. Also, the number 1 is neither a prime nor a composite number. Thus, it can be said that all prime numbers are greater than 1. All numbers except 1 are classified as prime and composite numbers. Composite numbers are those numbers that have more than two factors apart from 1 and the number itself.
Read More: NCERT Solutions for Class 6 Maths Playing With Numbers
| Table of Content |
Key Terms: Prime Number, Composite Number, Even Number, Factors, Even Prime Number, Number System, Whole Number
What is a Number?
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A number is an arithmetical value used to measure, label and count. These countable values make up the number system. Numbers can be divided into different categories or groups like Prime numbers, Composite numbers, Even and Odd numbers, Whole numbers, etc. Primary examples of numbers are 1, 2, 3, 4, 5, 6………….and so on.
- The counting numbers along with zero are called whole numbers.
- Natural numbers are numbers starting from 1 to infinity.
- Even numbers are those numbers that are completely divisible by 2 such as 4, 6, 8, 12, etc.
- Odd numbers are those numbers that are not completely divisible by 2 and leave a remainder such as 7, 9, 11, 15, etc.
- Prime numbers are those numbers that have only 2 factors which are 1 and the number itself.
- Composite numbers are defined as numbers with more than 2 factors.
Read More:
| Relevant Concepts | ||
|---|---|---|
| Is '1' a Prime Number? | Co Prime Numbers | Twin Primes |
| Prime Number Formula | Digits | Types of Numbers |
Is 2 a Prime Number?
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Yes, 2 is a special case of a prime number. 2 is definitely a Prime number as it has only two factors 1 and itself. The factors of 2 are 1 and 2 only. According to the definition of a prime number, a number that has only two factors or a number that is divisible by 1 and itself is called a prime number.
Is 2 a Prime Number?
Is 2 a Composite Number?
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No, 2 is not a composite number.
- Composite numbers are those numbers that have more than 2 factors.
- 2 has only two factors, i.e. 1 and 2.
- Thus, 2 is not a composite number because 2 doesn’t have more than 2 factors.
Is 2 the only Even Prime Number?
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Yes, 2 is the only even prime number. Even numbers are numbers that are divisible by 2. Two being divisible by itself becomes even in nature and as two is also prime in nature makes two a unique case of even prime numbers.
To verify the statement let’s examine other prime numbers.
- For example, let’s take number 3, number 3 is prime in nature as it has only two factors but 3 is not divisible by 2 which makes it an odd number.
- For another example let’s take 19, number 19 is a prime number as it has only two factors but 19 is not completely divisible by 2 which makes it an odd number.
Hence number 2 becomes a unique case of being the only even prime number.
Problem Statements about 2
Here are a few important problems about 2:
| Problem | Solution |
|---|---|
| Is 2 a Prime Number? | Yes |
| Is 2 a Composite Number? | No |
| What are the multiples of 2? | 2, 4, 6, 8, 10, 12, 14, 16, 18, 20… |
| Is 2 an Even Number? | Yes |
| Is 2 an Odd Number? | No |
| What is the Cube Root of 2? | 1.259921 |
| What is the Square Root of 2? | 1.414214 |
| Is 2 a Perfect Cube? | No |
| Is 2 a Perfect Square? | No |
What Kind of Number is 2?
The number 2 falls under the following categories of number:
- Natural number
- Whole number
- Positive integer
- Prime number
- Even number
- Rational number
Fun Facts about 2
Given below are a few fun facts about the number 2
- 2 is the only even prime number in the number system.
- 2 is the smallest prime number among all numbers.
- 2 is the smallest even number in the number system.
What is a Prime Number?
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Prime numbers are positive integers that have only two factors such numbers are called prime numbers.
- Prime numbers have only two factors those are 1 and itself.
- As prime numbers have 1 as one of their factors which means all prime numbers are positive that is greater than zero.
- 1 is neither a prime number nor a composite number.
- Some examples of Prime Numbers include 2, 3, 5, 7, 11, 13, 17, 19……etc.
Prime Numbers and Composite Numbers
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| Related Topics | ||
|---|---|---|
| Prime Factorization | Sum of Even Numbers | Number System Conversion |
| Real Numbers | Difference Between Whole Numbers and Natural Numbers | Number Lines |
List of Prime Numbers from 1 to 100
The prime numbers from 1 to 100 are as follows:
| Prime Numbers between 1 and 10 | 2, 3, 5, 7 |
| Prime Numbers between 10 and 20 | 11, 13, 17, 19 |
| Prime Numbers between 20 and 30 | 23, 29 |
| Prime Numbers between 30 and 40 | 31, 37 |
| Prime Numbers between 40 and 50 | 41, 43, 47 |
| Prime Numbers between 50 and 60 | 53, 59 |
| Prime Numbers between 60 and 70 | 61, 67 |
| Prime Numbers between 70 and 80 | 71, 73, 79 |
| Prime Numbers between 80 and 90 | 83, 89 |
| Prime Numbers between 90 and 100 | 97 |
What is a Composite Number?
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Composite numbers are positive integers that have more than two factors.
- All numbers except prime numbers are composite in nature.
- Composite numbers are the exact opposite of prime numbers.
- Generally, it is seen that even numbers are Composite in nature but 2 being an even number is prime in nature as it has only two factors 1 and itself.
Things to Remember
- 2 is the only even prime number present in the number system.
- Prime numbers are divisible by only 1 and itself which means they have only two factors.
- 2 is a unique number that has both an even as well as prime nature.
- 2 is the smallest prime number.
- Categories in which number 2 falls are Prime Number, Even Number, Natural Number, Positive Number, and Rational Number.
- 2 is also the smallest even number.
Sample Questions
Ques. What properties of number two make it a unique number? (1 Mark)
Ans. 2 is the only even prime number. It is even as it is divisible by 2 and it is prime as it is divisible by only 1 and itself. These properties make it unique in nature.
Ques. Are there any consecutive prime numbers? (1 Mark)
Ans. Yes, 2 and 3 are the only consecutive prime numbers.
Ques. Find all the Prime numbers between 1-100. (2 Marks)
Ans. Between 1-100, there are 25 numbers that have only two factors. They are as follows:
1, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 67, 71, 73, 79,83, 89, 97.
Ques. Find all the Prime numbers between 1-200. (2 Marks)
Ans. Between 1-200, there are 46 numbers that have only two factors. They are as follows:
1, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199.
Ques. Select Prime numbers between 5, 27, 39, 101, and 109. (2 Marks)
Ans. In the above-given numbers:
5 has two factors, 27 has more than two factors, 39 has more than two factors, 101 has only two factors, and 109 has only two factors so numbers 5, 101, and 107 are the prime numbers.
Ques. What is the smallest Prime number? (1 Mark)
Ans. 2 is the smallest prime number.
,Ques. What are the first ten Prime numbers? (1 Mark)
Ans. The first ten Prime numbers are 1, 3, 5, 7, 11, 13, 17, 19, 23, 29.
Ques. What is the sum of the first ten prime numbers? (2 Marks)
Ans. The first ten Prime numbers are 1, 3, 5, 7, 11, 13, 17, 19, 23, 29.
Sum of 1+3+5+7+11+13+17+19+23+29=128.
Ques. What is the sum of the first 7 prime numbers divided by 2? (2 Marks)
Ans. The first seven primes are 2, 3, 5, 7, 11, 13, and 17. 2 is the smallest prime number, and also the only even prime. Adding these seven prime numbers gives us a sum of 58, and 58/2 = 29.
<Ques. Which number is the Prime number in the following list 89, 196, 180, 121? (2 Marks)
Ans. For being a prime number a number must have only two factors
- 89- 1,89
- 196- 1,2,4,7,14,28,49,98,196
- 180- 1,2,3,4,5,6,9,10,12,15,18,20,30,36,45,60,90,180
- 121- 1,11,121
Clearly only 89 has two factors that is 1 and itself so 89 is the prime number.
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