# Aptitude - Numbers - Discussion

### Discussion :: Numbers - General Questions (Q.No.1)

1.

Which one of the following is not a prime number?

 [A]. 31 [B]. 61 [C]. 71 [D]. 91

Explanation:

91 is divisible by 7. So, it is not a prime number.

 Nishant said: (Sep 6, 2010) I know that prime numbers are of the form either 6k-1 or 6K+1 . Here 91 is of the form 6k+1 but still it is prime how come?

 Kulkarni said: (Sep 22, 2010) Here we have to notice that the above mentioned is not the general form of a prime number. There is no general form for prime no's, the above mentioned 6k+1 or 6k-1 will help you to find the prime no's but not for all the values of k.

 Dharmendra said: (Nov 9, 2010) What is the meaning of " k " ? 6k+1 or 6k-1 please explain.

 Tejas Mehta said: (Nov 29, 2010) 6k + 1 or 6k - 1 is a simplified form. Any prime number always satisfies this condition,where k can be 1,2,3...9. But plz Note: Every prime no can be written in the form of 6k+1,6K-1 But every no which can be written in the form of 6k+1,6k-1 are not necessarily prime. Here 91 can be written as 6k + 1 = 6(15) + 1 where k = 15, But it is not prime as it is divisible by 13,7.

 Niki said: (Jan 13, 2011) We can find whether a given number is prime by using the formula n*n>=p where n is the smallest number whose square is greater then or equal to p i:e the given number. if p is divisible by any of the prime numbers less than n then it is not a prime otherwise it is a prime number

 Prasath said: (Jan 27, 2011) Please give any one example.

 Prasath said: (Jan 27, 2011) n*n>=p plz give any example

 Santosh said: (Mar 12, 2011) Hiii friends .......just apply this formula to find the not prime no or prime no... n*n>=p 1)here P is the given no 2)find the squares which is > or = to the given no P 3)find the prime nos < or = n 4)check weather the given P no is divisible by prime nos which is < or =n 5)if divisible ....it mean it have more than two factors so given P is not a prime no. 6)if not divisible it mean the given no P is prime no

 Hariharan said: (Mar 24, 2011) Hi, santhosh. Please explain your formula with an example.

 Raji said: (Apr 25, 2011) Hi, i would like to share with a example to find 31 prime or not by the above formula it can be written as 6*6>=31(p) now upto 6 the prime nos are 2,3,5,7 31 is not divisble by any of these no, hence it would be a prime no

 Vengala Rao said: (Jul 1, 2011) Hai, santhosh your explanation is very nice.

 Santhosh said: (Aug 10, 2011) How you will consider 7 when you are checking for 31?

 Karthick said: (Sep 22, 2011) Thank you santhose:) your idea is too good to identify the prime no.

 Yogendra said: (Dec 9, 2011) Thanks santosh very much

 Manali said: (Jan 12, 2012) Thank you santosh.

 R.Deivasigamani said: (Feb 20, 2012) How to identify prime number and not prime number by easy method?

 Santosh(Pydah) said: (Feb 21, 2012) 91 is divided by 7 thats why it is not prime number.

 Shekhar said: (May 4, 2012) The number which is only divisible by itself and by 1, is called a prime number.

 Dilipkumar(Cse) said: (Jun 22, 2012) First you memorize these below numbers, 2, 3, 5, 7. 1--1379. 2--39. 3--17. 4--137. 5--39. 6--17. 7--139. 8--39. 9--7. These are the shortcuts for prime number. Lets see, 1--1379 means 11 is prime, 13 is prime, 17 is prime, 19 is prime. Likewise 2--39 means 23 is prime, 29 is prime. This is the easy way to memorize the prime number. Its very easy (just you have to memorize the above given no).

 Gomathi said: (Jul 22, 2012) Thank you santhosh. And explain with one or more examples please.

 Saheb Ali said: (Aug 24, 2012) @Raji thanks.

 Kishore Sulthana said: (Aug 31, 2012) Thank you dilipkumar

 Eswar said: (Oct 19, 2012) Can we use this shortcut for 3 and 4 digits?

 Puneet said: (Jun 8, 2013) @Dilipkumar(Cse). That is an awesome way to remember all prime numbers between 1 & 100. There is a pattern too.

 Hafiz Aqib said: (Jul 20, 2013) Table of Prime Number up to 1000. 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97 101 103 107 109 113 127 131 137 139 149 151 157 163 167 173 179 181 191 193 197 199 211 223 227 229 233 239 241 251 257 263 269 271 277 281 283 293 307 311 313 317 331 337 347 349 353 359 367 373 379 383 389 397 401 409 419 421 431 433 439 443 449 457 461 463 467 479 487 491 499 503 509 521 523 541 547 557 563 569 571 577 587 593 599 601 607 613 617 619 631 641 643 647 653 659 661 673 677 683 691 701 709 719 727 733 739 743 751 757 761 769 773 787 797 809 811 821 823 827 829 839 853 857 859 863 877 881 883 887 907 911 919 929 937 941 947 953 967 971 977 983 991 997

 Raja said: (Jul 25, 2013) @Santhosh @Raji thanks for help. But it only possible for some hundreds. When we find 9999 is prime no or not, It takes lot of time. n*n>= p. n*n>= 9999. Where n must be 100. So there are many prime no below 100. To divided by no. So it is not possible for all no. Please post another method if you knew.

 Konga said: (Sep 10, 2013) It is not possible for all numbers.

 Jeevitha said: (Sep 30, 2013) Please give me detailed explanation about prime number.

 K.Jagadeesh said: (Oct 1, 2013) If any given number is prime or not, how can u find out? here is one way to solve for that one. Step 1: Find the square root for given number. if it is not a perfect square take nearest number of that on. Ex: 91 is given. 8 is nearest square root (81) [91

 Ravindra said: (Dec 31, 2013) Simple meaning of prime no-"The number which is only divisible by itself and by 1, is called a prime number".

 Kimaya said: (Mar 21, 2014) The simple way is we should know tables to find which is a prime number.

 Priyanka.C(It) said: (Aug 18, 2014) Prime number is defined as divisible by "itself" and by "one" only.

 Balu said: (Aug 18, 2014) Hi, 11>square root of(91). (11*11=121 =>11^2 > square root of (91)). Then prime numbers below 11 are 2, 3, 5, 7 So 91 is divisible by 7. Hence 91 is not a prime number.

 Kishor said: (Sep 20, 2014) Prime number means, the number which is non actionable.

 Karthik said: (Sep 24, 2014) Number is 91. Take out last 1 and multiply by 2. 9 - (1*2) = 9 - 2 = 7. So it is divisible by 7. If we have more digits repeat the process. It is easy.

 Unaisvatts said: (Nov 17, 2014) @KARTHIK. If number is 97. 9-(2*7) = is not positive number.

 Kaviya said: (Apr 29, 2015) Which number is only divisible by 1 and the same number is called prime number.

 Shaziya said: (Jun 9, 2015) A negative number can be a prime number?

 Tinku Das said: (Jul 17, 2015) I want to know why 1 is not prime no?

 Manju Gouda said: (Jul 22, 2015) Basically a number is prime no. If it has exactly 2 distinct factors. For e.g for 13 factors are 13 and 1. So it is a prime number. But for 1 factors are 1 only. So it is not a prime number.

 Kavitha said: (Jul 22, 2015) Please, give me detailed explanation about the prime number and solve the steps one by one in the problem.

 Reshma said: (Jul 25, 2015) Explain one example with 3 digit number?

 Ramanna said: (Aug 21, 2015) What is prime number?

 Ramanna said: (Aug 21, 2015) What is prime number?

 Mahaboob Basha said: (Sep 16, 2015) Hi friends I have a doubt please clear it. What is the remainder when 1!+2!+3!+4!+5!+....+50! is divided by 5!?

 Shailendra Kumar said: (Sep 18, 2015) After 4! all the no is divisible by 5! so answer is (1+2+6+24)/6 = 33/6 = 3 (rem).

 Shilpa said: (Sep 25, 2015) 1!+2!+.....50!/5! = (1!+2!+......+50!) /1!+2!+.....+5! = 6!+7!+....+50!

 Narender Reddy said: (Jan 24, 2016) I want to clear explanation prime no's and not prime no's.

 Mahalakshmi said: (Feb 12, 2016) What is prime numbers how we have have to do calculation? Please explain me in detail.

 Dhruba said: (Mar 30, 2016) Sorry, I can't understand. Can anyone explain the answer with an easy method?

 Swati said: (May 4, 2016) @Dilipkumar(Cse). Is there any method to find the prime number between 1 to 1000?

 Hello said: (Jun 25, 2016) Thank you for explaining the problem.

 Poojarani said: (Jul 11, 2016) Thank you @Santosh.

 Shamanth said: (Aug 2, 2016) How can we find the number of prime numbers below 'n' numbers ?

 Akshay said: (Aug 13, 2016) Please, someone, know the method for divisibility of 6?

 Shailesh said: (Aug 17, 2016) If the number is divisible by 2 and 3 both, then it is divisible by 6.

 J.Krishnaveni said: (Sep 14, 2016) @Dilipkumar. Only for few numbers given for short cut in prime numbers. So please given for other numbers in the short cut method.

 Revanna P said: (Sep 25, 2016) How does 91 come?

 Shivani said: (Oct 5, 2016) Please give brief explanation of prime numbers.

 Nidhin M Z said: (Oct 6, 2016) 2, 3, 5, 7. 1--1379. 2--39. 3--17. 4--137. 5--39. 6--17. 7--139. 8--39. 9--7. These are the shortcuts for the prime number. Lets see, 1--1379 means 11 is prime, 13 is prime, 17 is prime, 19 is prime. Likewise 2--39 means 23 is prime, 29 is prime. This is the easy way to memorize the prime number. Its very easy (just you have to memorize the above given no).

 Nagasai said: (Oct 20, 2016) If the number is 91 when we divide by 2 it is equal to 45.5 numbers in between 45.5 to 91 cannot exactly divide 91 except itself so when we take below that numbers 45.5. It is easy to tell given is prime or not.

 Pooja.R.M said: (Dec 7, 2016) Thank you @Nidhin. Now I understand it easily.

 Deepika said: (Jan 17, 2017) @Nidhin. Thank you for this shortcut. It's really helpful. Will you tell me the shortcut to remember prime number above 100?

 Humaun said: (Mar 12, 2017) 2,5,8- 39 means 23, 29, 53,59,83,89 3-17 6-17 9-7 more easy to memorizing.

 Deepak Kumar said: (Apr 10, 2017) This is the easiest way to check prime number. Ex that 31, So put the nearest square of this number 25<31>36, so square of 31 is something 5. Something, then find the number below 5 prime number i.e. 2 and 3, now check 31 is divisible by this number or not if this is divisible then it is not the prime number, if this is not divisible then it is a prime number.

 Chandan said: (May 22, 2017) Identify Prime Number. 11 * 1 = 11. ODD .N 12=2*6, 3*4, 6*2, 12*1 etc.

 Renoop said: (Jul 5, 2017) 2,3,5,7,11 etc .... prime no. So 31 is not divided by 2,3,5,7,11.etc - so it is prime no. 61 is not divided by 2,3,5,7,11 -so it is prime no. 71 is not divided by 2,3,5,,7,11 so it is prime no. 91 is divided by 7 it is not prime no. So answer is D-91.

 Monika said: (Jul 16, 2017) Nice explanations. Thank you all.

 Sarthak Negi said: (Jul 27, 2017) We can use the elimination method here. The question says we need a number that is completely divisible by (2^32 + 1). So, a number that satisfies this condition will be larger than the given number. Option A and B are obviously smaller. Option C and D are the choices. On a closer analysis we find that even option c is smaller than the actual number. So we are left with option D as our final answer. You need to use your wit rather than calculation to solve a problem.

 Kishore said: (Aug 12, 2017) 13*7=91 so not prime number.

 Namrata said: (Aug 16, 2017) how to solve this question? Please tell me.

 Rajesh said: (Aug 29, 2017) The Prime number means any number is divisible by one and itself.

 Dilli Raja said: (Sep 19, 2017) For 3 numbers calculation: Let us find whether 149 is prime or not. [square root of 149= 12.20 < 13] prime numbers below 13 are 2,3,5,7,11. 149 is not exactly divisible by 2, because it don't has even number at the 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 don't has 0 or 5 at the end. 149 is not exactly divisible by 7,11. So, 149 is a prime number.

 Komal Gupta said: (Sep 20, 2017) @Karthick. I have not understood your process please explain me with the other examples.

 Deekshi said: (Oct 3, 2017) Code for prime numbers below 100 is 442233322321. 2,3,5,7 (4) 11,13,17,19 (4) 23,29 (2) 31,37 (2) 41,43,47 (3) 53,59 (2) 61,67 (20 71,73,79 (3) 83,89 (2) 97 (1)

 Prabhakar Gupta said: (Oct 4, 2017) 91is not a prime no. Because it is divisible by 13.

 V Ramesh said: (Jun 21, 2018) Prime number is nothing but it is divisible by one and itself that type of numbers called prime numbers.

 Darshan said: (Jul 7, 2018) Thanks @Nidhin.

 Annapurna said: (Sep 3, 2018) Thank you @Santosh.

 Sharmi said: (Sep 26, 2018) Thank you @Dilipkumar.

 Kranthi Kumar said: (Jan 22, 2019) Please give me the clear explanation of the answer.

 Nithish said: (Feb 3, 2019) Prime number is nothing but a number divisible only by one and that number. But 91 is divisible by Seven. So it's not a prime number.

 Sanket said: (Jun 6, 2019) Thanks all.

 Roop said: (Jun 13, 2019) Thanks all for explaining.

 Sangeetha said: (Aug 4, 2019) Thanks all.

 Rameshwar said: (Aug 4, 2019) Thanks all.

 Kavitha said: (Aug 24, 2019) When we apply the condition. n*n >=p for 91! How does that work? (10*10>=91. Factors of 10 -2, 5, 10. So how is this condition satisfiying for the above question).?

 Jyoti said: (Nov 14, 2019) 91 is the correct answer.

 Sagarganeshkar said: (Feb 28, 2020) It is very easy by divisibility rules.

 Jagadees said: (Jul 1, 2020) Thanks @Dilipkumar and @Santosh.

 Swathi said: (Oct 7, 2020) Thanks all.

 Pooja said: (Oct 22, 2020) n*n>=p in this form, how take that value by comparing p? Please explain anyone.

 Harika said: (Jan 19, 2021) 31 is the prime number.

 Tharun said: (Mar 19, 2021) 91 is correct because the prime number is one which is having two distinct factors so, that 91 having more than two factors.

 Sindhuja B said: (May 31, 2021) The Question is "which is not a prime number". In a very simple way how do we check whether a number is prime or not, . The number should be divisible by one & the number it self right!. Now see their options, that are, . 31. - is a prime number which can only be divided 1 & the number itself. 61. - same here. 71. - here too. 91. - is divisible by 1, 7, 91. So, among other options, 91 is not a prime number.

 Sharma said: (Aug 21, 2021) 91 prime or not. Which square number is exceeds 91? 10 ^2 right. So let's take a prime number which is less than 10. 2, 3, 5, 7. Check the given number is divisible by 2, 3, 5, 7. If it is divisible then it is not a prime number. If not that would be a prime number.

 Jitu said: (Sep 15, 2021) Why only 91 is not a prime number? In this case, 71 is also divisible by 3.