How To Find Prime Numbers and How To Check if a Number is Prime

                How to find if a number is prime? We get questions on this topic in some competitive exams. Deciding whether a number is prime number or not is not a simple task if it is bigger number. So, some techniques are needed to tell if the number is prime. This is what you are looking for, then you are in right place. Because I have covered everything you need to know about Prime numbers.


 Contents : 


1. Prime Number Definition
2. Prime Factorization – Finding Prime Factors
3. Finding all prime numbers between 1 and 100 in a simple way
4. How to check if a number is Prime
5. Some facts about prime numbers
6. prime numbers upto 1000


How To Check if a Number is Prime - Puzzles/Aptitude/Reasoning/Brainteasers


 Prime Number Definition : 


A Number which is divisible by 1 and the number itself is called as PRIME NUMBER.
Prime number must be a positive integer and it should be greater than 1.

Ex :

17 is divisible by 1 and 17 only, So, it is prime number.

15 is divisible by 1,3,5,15. So, it is not prime number.  

  Prime Factorization – Finding Prime Factors :  


Factors of any number should be prime numbers in prime factorization.
Factors are numbers which are multiplied to get original number.
2 * 3  =  6   => 2, 3 are factors of 6. They are also prime factors of 6.
54  = 9 * 6  => 9,6 are factors of 54, but they are not prime factors.

Factor Tree : 

Factor Tree can be used to get prime factors of a number.

How To Check if a Number is Prime - Finding Prime Factors- Puzzles/Aptitude/Reasoning/Brainteasers

2 * 3 * 3 * 3 = 54 => this is how we do prime factorization.
2,3 are prime factors of 54.

  Finding all prime numbers between 1 and 100 in a simple way :  


  25 prime numbers are there in between 1 and 100.
2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97…………

Finding all prime numbers between 1 and 100 in a simple way - Puzzles/Aptitude/Reasoning/Brainteasers


  1. First arrange numbers in a table like shown in figure.
  2. Enter 6 numbers in each row until the last number (in this it is 100) reaches.
  3. Start with 2 which is greater than 1.
  4. Round off number 2 and strike off entire column until the end.
  5. Similarly strike off 4th column and 6th column as they are divisible by 2.
  6. Now round off next number 3 and strike off entire column until end.
  7. 4 is gone.
  8. Now round off next number 5 and strike off numbers in inclined fashion as shown in figure. When a striking off ends in some row, start again striking off with number in another end  which is divisible by 5 in a row parallel to previous strike off line as shown in figure.
  9. 6 is gone.
  10. Now round off number 7 and strike off numbers as we did in case of number 5.
  11. 8,9,10 are gone.
  12. Stop at this point. Wonder why do we need to stop??
  13. It’s a trick that we have to do this procedure until we reach square root of bigger number.
  14. This technique was developed in 3rd century B.C.

  How To check if a Number is Prime :  


Divide the given number with every number below it except 1 and the number itself. 
Check whether the given number is divisible by any of the numbers below it. 
If it is not divisible by any number then it is prime number.

"Divisible by" means when you divide the whole number with another whole number result should be whole number with remainder zero.

Actually you don’t need to divide with all numbers.

First check whether it is divisible by 2 or not. 
Next check with 3, 5, 7, 11,13…..
Check divisibility only with prime numbers.

Here also you don’t need to divide with all prime numbers below it.

Let p be the given number.
Find a number n greater than \(~\sqrt{p}\)
Find prime numbers below n and divide p with only those prime numbers below n.

Actually, we used the same procedure in the above figure of finding all prime numbers upto 100.

Ex : 1 - Number is 149

Let us find whether 149 is prime or not.
\[\sqrt{149}= 12.20 < 13\]
prime numbers below 13 are 2,3,5,7,11….
149 is not exactly divisible by 2, because it dont has even number at end.
149 is not exactly divisible by 3, because the sum of numbers 1+4+9= 14 is not divisible by 3.
149 is not exactly divisible by 5, because it dont has 0 or 5 at end.
149 is not exactly divisible by 7,11.
 So, 149 is prime number…


Ex: 2 - number is 631


Let us find whether 631 is prime or not.
\[\sqrt{631}= 25.11 < 26\]
prime numbers below 26 are 2,3,5,7,11,13,17,19,23….
631 is not exactly divisible by 2,3,5,7,11,13,17,19,23…
So, 631 is prime number…

For easy divisibility checking, you should know the divisibility rules. 


  Some Facts on Prime Numbers:    



Co Primes:        
       
H.C.F. of two numbers in one set should be 1.
Ex: (2,3),(4,5),(6,7),(11,15)

If a number N is divisible by two numbers a and b, where a, b are co primes, then N is divisible by ab.

Twin Primes:

Difference between prime numbers in one set should be 2.
Ex: (3,5),(5,7),(11,13),(17,19),(31,33) 

If a Number M is a prime number and N is a next prime number, the average difference between M and N is “ ln(M) ” [natural logarithm of M]
  • 2 is the only one prime even number.
  • Numbers greater than 1 and which are not prime numbers are composite numbers.
  • Some probabilistic methods are available for checking big prime numbers. 

  Prime Numbers upto 1000 : 


Here is the list of prime numbers upto 1000 for your reference.


 How To Find Prime Numbers - Prime Numbers upto 1000 - Puzzles/Aptitude/Reasoning/Brainteasers


Thats all about Prime Numbers.

Read again about Basic Number theory

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Marks and Time puzzle 59

Find solution for this in puzzles/aptitude/reasoning/brainteasers.

A teacher gave 13 marks to one student and 12 marks to another student in one exam. 
Can you tell the TIME by using the above sentence ????


1.45
The teacher gave a total of 25 marks to two students. 25 is a quarter.
So, teacher gave “Quarter to Two”.

Time format to “Quarter to Two” is 1.45.

Birthday Brainteaser 58

Find solution for  Birthday Brainteaser 58 in puzzles/aptitude/reasoning/brainteasers

The day before yesterday I was 25.
The next year I will be 28.
This is true only one day in a year.
What day is my Birthday ?



My birthday is on December 31. I am telling this on January 1.
Day before yesterday (dec 30)    = I am 25
Present day (January 1)               = I am 26
this year december 31                 = I will be 27.

Next year december 31               = I will be 28.

Simple Maths Question 57

get an answer for Simple Maths Question 57 in puzzles/aptitude/reasoning/brainteasers

What Mathematical symbol can be placed in between 3 and 7, to get a number which lies in between 3 and 7???


Exact Answer      = 3.7 (Decimal symbol)
Related Answer  = 3cot7 =3 * 1.14 = 3.42

Litres Measuring Puzzle 56

find solution for Litres Measuring Puzzle 56 in puzzles/Aptitude/reasoning/brainteaser


You have 3 litre bottle and 5 litre bottle. How can you measure 4 litres of water by using 3Lt and 5Lt bottles???



Solution 1 :

1. First fill 3Lt bottle completely and pour 3 litres into 5Lt bottle. 
2. Again fill 3Lt bottle completely. now pour 2 litres into 5Lt bottle until it becomes full.
3. Now empty 5Lt bottle.
4. Pour remaining 1 litre in 3Lt bottle into 5Lt bottle.
5. Now again fill 3Lt bottle completely and pour 3 litres into 5Lt bottle.
6. Now you have 4 litres in 5Lt bottle. That's it. 

Solution 2 :

1. First fill 5Lt bottle completely and pour 3 litres into 3Lt bottle.
2. Empty 3Lt bottle.
3. Pour remaining 2 litres in  5Lt bottle into 3Lt bottle.
4. Again fill 5Lt bottle completely and pour 1 litre into 3 Lt bottle until it becomes full.
5. Now you have 4 litres in 5Lt bottle. That's it.

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Missing Rupee Brain Teaser 55

mind puzzles and riddles with answers and solutions

3 Friends went to a shop and purchased 3 toys. Each person paid Rs.10 which is the cost of one toy. So, they paid Rs.30 i.e. total amount. Shop owner gave a discount of Rs.5 on the total purchase of 3 toys for Rs.30. Then, among Rs.5, Each person has taken Rs.1 and remaining Rs.2 given to the beggar beside the shop.
Now, the effective amount paid by each person is Rs.9 and the amount given to beggar is Rs.2. So, total effective amount paid is 9*3 = 27 and the amount given to beggar is Rs.2, thus the total is Rs.29. Where has the other Rs.1 gone from the original Rs.30 ?????


The logic is payments should be equal to receipts. we cannot add amount paid by persons and amount given to beggar and compare it to Rs.30.
The total amount paid is Rs.27. So, from Rs.27, shop owner received Rs.25 and beggar received Rs. 2. Thus, payments are equal to receipts.

Magic Room Riddle 54



You are in one magic room. That room is having two doors. one door leads to death and another door is safe. If you ask a question, one door always tells truth and another door always lies and you don't know which one tells truth and which one lies. You can ask only one question to only one door and you must get through the safe door. So, how will you manage to get through the safe door ?? Which question would you ask and To which door you would ask ????
 
Answer : Just go to any one door and ask, "what the other door would tell if you asked which door is safe?" and go through another door. That's it. So, the question is important and the door to which you are asking doesn't matters.
 Still confused.. Let me know it in comments...

Number of Days Puzzle 53

maths logical puzzle and brain teasers with answer
 A man is climbing up a mountain which is inclined. He has to travel 100 km to reach top of mountain. Every day He climbs up 2 km forward in day time. Exhausted, he then takes rest there at night time. At night, while he is asleep, he slips down 1 km backward because mountain is inclined.
Then how many days does it take him to reach mountain top ????




Answer : 99 days
Solution : Each day, Total progress = 2 km - 1 km = 1 km
So, 98 days = 98 Kms.
On 99th day he can reach mountain top by travelling 2 km in day time.
So, answer is 99 days.

Decision Making PUZZLE 52

Solve simple and Logic puzzle with solution in puzzles9


For Rs.1 You get 40 Bananas.
For Rs.3 you get 1 Mango.
For RS.5 you get 1 Apple.

Now you want to get 100 fruites for Rs.100.

So, How many Bananas, Mangoes and Apples will you buy ??

                                                                         


Rs.95 - 19 Apples
Rs.3  - 1 Mango
Rs.2  - 80 Banans

Total 100 Fruites for RS.100.

Basic Number Theory for Problems on numbers in Aptitude

         Hi everyone, you may not get direct questions on this in any aptitude type test. But, by knowing this number system basics you can be able to solve some silly questions on numbers in some simple tests. So, Get your basics brushed up with this.

0,1,2,3,4,5,6,7,8,9      -    Digits
group of digits             -    Numbers


basic number theory for number problems



Natural numbers                    :    1,2,3,4,5,6,7,8,9,10,11………………….
Whole numbers                     :    0,1,2,3,4,5,6,7,8,9,10,11,12…………….
Integers                                 :    …………-4,-3,-2,-1,0,1,2,3,4………………….
        Positive integers                     :   1,2,3,4,5,6,7………….
        Negative integers                   :   ………….-7,-6,-5,-4,-3,-2,-1
        Non positive integers              :   0,-1,-2,-3,-4…….
        Non negative integers             :   0,1,2,3,4,5,6…………………
                            
0 is neither positive nor negative.

Even numbers                :         A number divisible by 2
                                                      2,4,6,8,10,12,14,16,18,20………………
Odd numbers                 :         A number not divisible by 2.
                                                      1,3,5,7,9,11,1,3,15,17,19,21……………………
Prime numbers               :         A number having exactly 2 factors, namely 1 and the number itself.
2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97………
2 is the only one prime even number.
25 prime numbers are there in between 1 and 100.
Composite numbers        :          Numbers greater than 1 which are not prime numbers.
                                                      4,6,8,9,10,12,14,15…………….
0,1 are neither prime nor composite.
Co primes                       :           H.C.F. of two numbers should be 1. 
                                                       (2,3),(4,5),(6,7),(11,15)
Twin primes                     :           Difference between prime numbers in one set should be 2.
                                                       (3,5),(5,7),(11,13),(17,19),(31,33)

If a number N is divisible by two numbers a and b, where a, b are co primes, then N is divisible by ab.
Ex :  72 is divisible by 2 and 3, where (2,3) are co primes. So, 72 is divisible by 6 i.e. (2×3)

Face value         :    The actual value of a digit in the given number
Place value        :    This value varies depends upon place of digit in a given number.
Ex :  In 895473,
           Face value of 3 is 3 , face value of 9 is 9.
             Place value of 3 = 3*1 = 3
             Place value of 7 = 7*10 = 70
             Place value of 4 = 4*100 = 400
             Place value of 9 = 9 * 10000 = 90000

Division rule :
                     Dividend = (Divisor × Quotient) + Remainder 


Ex :  14 = (3 × 4) + 2
      14  =   Dividend
       3   =   Divisor
       4   =   Quotient
       2   =   Reminder

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Missing Number Problem 51

FIND THE MISSING NUMBER IN THE BELOW NUMBER SEQUENCE APTITUDE PUZZLE

FIND MISSING NUMBER IN NUMBER SEQUENCE PUZZLE


                                                                     
ANSWER : 8

SOLUTION : 

In the above puzzle, sum of corner numbers and sum of middle numbers is equal to 34.
10 + 9 + 8 + 7 = 34 ;
15 + 5 + 6 + 8 = 34 ;

So, answer is 8.



Number Missing Puzzle 50

Find the missing number in the below number sequence puzzle

puzzles9 - puzzle 50 - find the missing number in number sequence puzzle

                                                                   


Answer : 9

Solution : 

In the above puzzle, in each row, subtract the second number from first number to get the third number and add the first two numbers to get the fourth number.

5 - 2 = 3 ; 5 + 2 = 7 ;
6 - 3 = 3 ; 6 + 3 = 9 ;
4 - 1 = 3 ; 4 + 1 = 5 ;
8 - 1 = 7 ; 8 + 1 = 9 ;

So, answer is 9.


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