|Quantitative Aptitude Important Formulas Logical ReasoningGeneral Knowledge of MPGeneral Knowledge of India|
Numbers - Important Formulas,Tricks and Examples
The common number system is decimal number system.
Types of Numbers
Natural Numbers:The numbers that are used for counting called Natural Numbers.These are infinite and start from the number 1 .
Whole numbers:The whole numbers are just all the natural numbers plus zero.
Integers: Integers incorporate all positive and negative numbers with zero.
Even Numbers: An even number is one that can be divided evenly by two leaving no remainder, such as 2, 4, 6, and 8.
Odd Numbers: An odd number is one that does not divide evenly by two, such as 1, 3, 5, and 7.
Rational Numbers: All numbers of the form p/q where p and q are integers (q ≠ 0) called Rational numbers.
Irrational Numbers: Irrational numbers are the opposite of rational numbers. An irrational number cannot be written as a fraction as p/q where a and b are integers.
Real numbers: Real numbers include counting numbers, whole numbers, integers, rational numbers and irrational numbers.
Prime Number: A prime number is a number which can be divided only by 1 and itself. The prime number has only two factors, 1 and itself.
Composite Number: A Composite Number is a number which can be divided evenly. Any composite number has additional factors than 1 and itself.
Co-primes or Relatively prime numbers: A pair of numbers not having any common factors other than 1 or –1. (Or alternatively their greatest common factor is 1 or –1)
Twin Primes: A pair of prime numbers is said to be twin primes if they differ by 2.
(a+b)2 = a2 + 2ab + b2
(a+b)2 - (a-b)2 = 4ab
a2-b2 = (a-b)(a+b)
(a+b)3 = a3+b3+3ab(a+b) = a3+b3+3a2b+3ab2
a3+b3 =(a+b)3-3ab(a+b) = (a+b)(a2-ab+b2)
Test of Divisibility
Divisibility By 2 : A number is divisible by 2, if its unit's digit is zero or even (2, 4, 6, 8..).
Divisibility By 3 : A number is divisible by 3, if the sum of its digits is divisible by 3.
Divisibility By 4 : A number is divisible by 4, if the number formed by the last two digits is divisible by 4.
Divisibility By 5 : A number is divisible by 5, if its unit's digit is either 0 or 5.
Divisibility By 6 : A number is divisible by 6, if it is divisible by both 2 and 3.
Divisibility By 8 : A number is divisible by 8, if the number formed by the last three digits of the given number is divisible by 8.
Divisibility By 9 : A number is divisible by 9, if the sum of its digits is divisible
Divisibility By 10 : A number is divisible by 10, if it ends with 0.
Divisibility By 11 : A number is divisible by 11, if the difference of the sum of its digits at odd places and the sum of its digits at even places, is either 0 or a number divisible by 11.
Divisibility By 12: A number is divisible By 12 if the number is divisible By both 4 and 3.
Divisibility By 13: A number is divisible By 13 if its unit’s place digit is multiplied By 4 and added to the remaining digits and the number obtained is divisible By 13.
Divisibility By 14: A number is divisible By 14 if the number is divisible By both 2 and 7.
Divisibility By 15: A number is divisible By 15 if the number is divisible By both 3 and 5.
Divisibility By 16: A number is divisible By 16 if its last 4 digits is divisible By 16 or if the last four digits are zeros.
Divisibility By 17: A number is divisible By 17 if its unit’s place digit is multiplied By 5 and subtracted from the remaining digits and the number obtained is divisible By 17.
Divisibility By 18: A number is divisible By 18 if the number is divisible By both 2 and 9.
Divisibility By 19: A number is divisible By 19 if its unit’s place digit is multiplied By 2 and added to the remaining digits and the number obtained is divisible By 19.
Divisibility By 20: A number is divisible by 20 if it is divisible by 10 and the tens digit is even.
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