Aptitude - Numbers - Discussion

Thanks both of you for the clear explanations. @Hafiz and@ Dilip.

The prime number definition: the numbers which is divisible 1 and itself. or the number contains only 2 factors are prime numbers.

A.31 = 1,31 only 2 factors so it is a prime number.
B.61 = 1,61
C.71 = 1,71
D.91 = 1,7,13,91 In this option D there are more than 2 factors.
And 91 divisible 7 which is 13.
91/7= 13,
so, option D is the correct answer.

91 is correct because the prime number is one which is having two distinct factors so, that 91 having more than two factors.

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.

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

No, @Jitu,

71 will not be divisible by 3.

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).

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<x^2]

Step 2:

Write all prime numbers below that square root number.

2 3 5 7

Step 3:

If the given number(91) is not divisible with any one of the above numbers(2 3 5 7) then that number is prime number otherwise it's not.

Nice explanations. Thank you all.

91 is the correct answer.