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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About the author: SAI MOHAN REDDY

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