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There has been a lot of discussion on Is '1' a prime number or a composite number. It can be said that 1 is a distinctive number and is considered a building block for any other number.
- There is a lot of ambiguity regarding counting 1 in the set of prime numbers.
- G.H Hardy, a great mathematician, even had the same confusion.
- He included 1 in the list of prime numbers for his book "A Course in Pure Mathematics" till 1933.
Before starting the topic, first, understand the terms prime number and composite number. A prime number is one with only two factors, whereas a composite number has more than two.
- A factor is a value that can divide a number or an expression into equal parts.
- These are two types of numbers that differ based on the number of variables.
- The number 1 has only one divisor, which is the number itself.
Key Terms: Is ‘1’ a Prime Number, Numbers, Number system, Prime numbers, Composite numbers, Factors, Integer, Whole number, Odd Number, Divisors, Co-prime Numbers
Is 1 a Prime Number?
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The answer to the current question is No. It means 1 is neither a major prime nor a composite number. The divisors for number one are 1 and the number itself. Both the divisors are positive.
- In accordance with the notion, prime numbers are defined as any number with just two positive divisors.
- 2 is considered the smallest number that satisfies the notion of prime numbers.
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|---|---|---|
| Important Questions on Real Numbers | Natural Numbers and Whole Numbers | Area of Rectangle |
| Area of Square | Addition and Subtraction of Integers | Integers as Exponents |
What are Prime Numbers?
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A prime number is one that contains exactly two factors, namely the number itself and the number '1.' In simpler terms, they are positive integers that consist of only two factors, namely 1 and the number itself.
- These numbers are greater than one.
- The concept of these numbers was first introduced by Greek mathematicians such as Euclid.
- The two famous theorems used for prime number distribution include the prime number theorem and the Riemann zeta function.
- Tests of Divisibility and Factorization are two methods to find these types of numbers.
Example of What are Prime Numbers?Example 1: Number 3 is a prime number since it can only be split by two numbers: 1 and 3. Example 2: Similarly, the digits 2, 5, 7, 11, 13, and 17 are prime numbers. |
What are Composite Numbers?
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A composite number has more than two factors, which indicates that it can be divided by at least one integer or number in addition to the number 1 and itself.
- Natural numbers comes under the category of composite numbers.
- They are also known as composites.
- These numbers can be used as integers when multiplied by two smallest positive integers.
- Odd Composite Numbers and Even Composite Numbers are two types of composite numbers.
- It is made up of two or more prime numbers.
Example of What are Composite Numbers?Example: As it can be divided by 1, 2, 3, 4, 6, and 12, 12 is an example of a composite number. As a result, the number '12' includes six factors. |
What is 1 called if it is not a Prime Number?
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The number one is neither prime nor composite. In mathematics, the number 1 can be found in a variety of categories. The number of factors of 1 is less than 2.
As a result, one can be referred to by any of the following numbers:
- Natural Numbers
- Rational Numbers
- Positive Integers
- Odd Numbers
- Whole Numbers
Why is 1 not a Composite Number?
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The answer to this question can be found in the definition of composite numbers. A composite number is a natural number containing more than two positive elements, according to the definition.
- However, 1 has only one factor, which is one itself.
- As a result, one cannot be considered a composite number.
Lesson Summary
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The summary of Is ‘1’ a Prime Number are as follows:
| Category | Data |
|---|---|
| Is 1 a prime number? | No, 1 is not a prime number. |
| Is 1 a composite number? | No, 1 is not a composite number. |
| What are the factors of 1? | 1 has only one factor that is one itself. |
Things to Remember
- One does not belong to the category of prime numbers and composite numbers.
- 2 is the smallest even prime number.
- For values of n between 0 and 39 inclusive, Euler identified a polynomial n2 + n + 41 that gives prime integers.
- A palindrome prime is a prime number that produces the same result when read backwards.
- A composite number is always a perfect cube.
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Sample Questions
Ques: What is ‘1’ called? (2 marks)
Ans: 1 (also known as unit or unity) can be a number as well as a numerical digit used to represent that number in numbers. It symbolises a single thing, the counting or measurement unit. A line segment of unit length, for example, could be a line segment of length 1. The smallest and first positive integer is 1.
Ques: Who Is the Inventor of 1? (2 marks)
Ans: The set of 10 symbols in Hindu and Arabic numerals are - 1, 2, 3, 4, 5, 6, 7, 8, 9, 0 - They represent the numbers within the decimal numeration system. Around the 12th century, they were brought to the rest of Europe through the writings of Middle Eastern mathematicians, particularly the al-Khwarizmi and al-Kindi.
Ques: Is the number one a prime or a co-prime number? (2 marks)
Ans: The numbers 1 and -1 are the only integers that are coprime with every other integer, as well as the only integers that are coprime with 0. a and b are coprime in a variety of situations: There is no prime that divides both a and b.
Ques: What are the answer to following question: (A) Make a list of all prime numbers that are smaller than 15.
(B) Do the digits 2, 4, 6, 8, 10, 12, 14... have a pattern to them? (2 marks)
Ans: (A) Using the Sieve Method, the needed prime integers can be written as 2, 3, 5, 7, 11, and 13.
(B) You'll see that they're all multiples of two. These are referred to as even numbers. Odd numbers are the remaining numbers 1, 3, 5, 7, 9, 11, and so on.
Ques: Which are all prime numbers from 1 to 100? (2 marks)
Ans: All prime numbers from 1 to 100 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: What are the answer to following question: (A) Find first ten prime numbers?
(B) Find sum of first ten prime numbers? (2 marks)
Ans: (A) 1, 3, 5, 7, 11, 13, 17, 19, 23, 29.
(B) Sum is 1+3+5+7+11+13+17+19+23+29=128.
Ques. What is the sum of the third and seventh prime numbers? (2 marks)
Ans: The third prime number is 5 and the seventh prime number is 17. Then sum of third and seventh prime number is 22.
Ques: What are the ten multiples of 26 and 20? (2 marks)
Ans: The multiples of 26 are 26, 52, 78, 104, 130, 156, 182, 208, 234, 260
The multiples of 20 are 20, 40, 60, 80, 100, 120, 140, 160, 180, 200
Ques: What are the prime numbers that lie between 1 to 200? (2 marks)
Ans: The prime numbers that lie between 1 to 200 are 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. Therea are total of 44 numbers.
Ques: Which number is the Prime number in the following list 23,12,28,117? (2 marks)
Ans: The list of numbers are as follows:
- 23- 1,23
- 12- 1, 2, 3, 4, 6, 12
- 28- 1, 2, 4, 7, 14, 28
- 117- 1, 3, 9, 13, 39, 117
Ques: What is the factor and prime factors of 961, 361 and 465 ? (3 marks)
Ans: The list is as follows:
| Number | Factor | Prime Factors |
|---|---|---|
| 961 | 1, 31, 961 | 31 |
| 361 | 1, 19, 361 | 19 |
| 465 | 1, 3, 5, 15, 31, 93, 155, 465 | 3,5,31 |
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