Is 101 A Prime Number?

Every mathematical number can be divided into two categories: Prime number and Composite number. While Composite Numbers can be defined as whole numbers which possess more than two factors, the Prime Numbers are slightly different. It is very easy to find out if any given number is a prime number or not. You just need to find out an integer that can evenly divide the said number. However, the integer should not be 1 or the number itself. Now, coming to the question of is 101 a prime number?, the answer is ‘Yes’. Let us find out in detail about how and why is 101 a prime? 


What is a Factor of a Number?

Factors are basically the numbers that you multiply in order to get another number. Thus, the two basic numbers you require for getting the product answer are the factors of the said product. This concept can be really helpful in understanding ‘is 101 a prime number’ as well. For example: 

  • What will be the factors of 15?

Answer: factors of 15 = 3 and 5 because 15 is a direct product you get when you multiply 3 and 5; 3 X 5.


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The concept of factors is very important to understand the basic difference between Prime Numbers and Composite Numbers and to determine whether a number is a prime or not. This concept would help you get the answer to the question of ‘is 101 a prime number?’ easily.


Now, coming back to Prime numbers.


What Are Prime Numbers?

Similar to atoms being the building blocks of elements in Science, Prime Numbers are nothing short than building blocks in Mathematics. You can define a Prime Number as a whole number who can possess only 2 factors, 1 and the number itself. For example:


Well, 11 is a Prime Number because you can divide 11 by only two numbers: 1 and 11 itself. On the other hand, 8 is a composite number because for 8, you get more factors: 8 = 2 X 4, 1 X 8. The same concept applies to the logic behind ‘Is 101 prime or composite number?


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The first 10 Prime numbers in the number list are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29. Following the list, you can get an answer to the question also, ‘is 101 a prime number.’?


Example

2 = 1 x 2; the only factors of 2 are 1 and 2;

3 = 1 x 3; the only factors of 3 are 1 and 3;

5 = 1 X 5, the only factors of 5 are 1 and 5;

7 = 1 X 7, the only factors of 7 are 1 and 7;


How to Find if the given number is a Prime Number?

To find out whether a given number is a prime number of not, you need to first try dividing it by 2. Did you get a whole number? If the answer is ‘Yes’, it cannot be a Prime Number. However, if you do not get a whole number on dividing by 2, try to divide it by prime numbers, i.e. 3, 5, 7, 11, etc. 


Table of Prime Number Upto 1,000


1

2

3

5

7

9

11

13

17

19

23

29

31

37

41

43

47

53

59

61

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

211

223

227

229

233

239

241

251

257

263

269

271

277

281

283

293

307

311

313

317

331

337

347

349

353

359

367

373

379

383

389

397

401

409

419

421

431

433

439

443

449

457

461

463

467

479

487

491

499

503

509

521

523

541

547

557

563

569

571

577

587

593

599

601

607

613

617

619

631

641

643

647

653

659

661

673

677

683

691

701

709

719

727

733

739

743

751

757

761

769

773

787

797

809

811

821

823

827

829

839

853

857

859

863

877

881

883

887

907

911

919

929

937

941

953

967

971

977

983

991

997





The table represents prime numbers between 1 and 1000.


Why Is 101 a Prime Number?

Based on the concepts mentioned above, it can be rightly said that 101 is a prime number. The reason being that 101  has only 2 factors, i.e., 1 and 101 itself.  Since you cannot get 101 as a product by multiplying any other two numbers, 101 is a Prime Number. You can also follow the below-mentioned steps to determine whether 101 is a prime or not. 


Step 1: Firstly, determine whether the ‘Units’ digit of the said number is either 2, 4, 6, 8, or in other words divisible by 2. If this is the case, then the given number is not a Prime Number. Since the ‘Units’ digit in 101 is not divisible by 2, it is a Prime Number.


Step 2: Check the divisibility of 101 with digits below 10.


Step 3: Check whether the sum of the digits in 101, i.e. 1 + 0 + 1 = 2 can be divided by 3.


Step 4: Take the factors test. Since 101 has no other factors than 1 and 101, it is Prime Number.


Solved Examples

Example 1: Is 63 A Prime Number?

Solution: No, 63 is Not a Prime Number.


63 is a multiple of 1, 3, 7, 9, 21. Thus, since it has more than two multiple, i.e. 1 and 63, it is not a prime number.


Example 2: Is 3 A Prime Number?

Solution: Yes, 3 is a Prime Number.


3 has only two multiple, i.e. 1 and 3, thus, it is a Prime Number.

FAQ (Frequently Asked Questions)

1. Is 101 Divisible By Any Number?

Well, 101 can be divided by only two numbers, 1 and 101 itself. There are no other numbers that can divide 101 and this is the main reason why 101 is a Prime number and not a Composite Number. Thus, the factors of 101 are 1 and 101. Thus, when you want to know, is 101 prime or composite number, you can surely say that it is a Prime Number based on the factors test as it has only two factors and is not divisible by any other number than 1 or 101. In fact, this is the main logic behind determining the Prime Number quotient of a particular number.

2. What Are The Basic Differences Between Prime Number and Composite Number?

The main difference between a Prime Number and a Composite Number is basically factors. You can determine the status of a number by calculating its factors. Prime numbers have only two factors, 1 and the number itself. For example, 1, 3, 5, 7, 9, etc. On the other hand, composite numbers have more than two factors. A composite number can be divided by 1, the number itself, and any other number as well. For example, 4, 6, 8, 10, etc. Understanding this difference is necessary to get better clarity over integers, factors, and other mathematical concepts.