Number System-2

0- insignificant digit
others 1,2,3,4,5, ... significant digits

Numeral : Group of figures, representing a number is called a numeral

Natural Nos: N = {1,2,3...]
Whole Nos: N = {0,1,2,3...]
Integers: N \ { -3,-2,-1,0,1,2,3, ]

Rational No= When the nos are written in fractions 1/2, 3/4, 8/9 (Where a and b are integers and b is not = 0, eg a/b)

Irrational Nos: When a number cannot be written as a/b eg. sqrt (3) or sqrt(2)

Real No= Rational + Irrational
Comosite No= A number other than 1 which is not prime is a composite number
Even No.
Odd No.
Consecutive Nos= 6,7,8
Prime Numbers= other than 1 is prime if it is divisible by 1 and itself only

Prime numbers upto 100 are (2,3,5,7,11,13,17,19,23,29,31,37,41,43,53,59,61,67,71,73,79,83,89,97)

Number System

Rules of Divisibility


Divisibility by 2- Last Digit must be even or 0
Divisibility by 3- Sum of Digits - must be divisible by 3
Divisibility by 4- Last 2 digits divisible by 4 or two or more zeros at the end
Divisibility by 5- Last Digit should be either 0 or 5
Divisiiblity by 6- The number should be divisible by 3 AND 2

(divisibility by mxn--> then number should be divisible by m and n)

Divisibility by 7--> Remember the number (-2). Thus to check divisibility of 112 by 7, take the last digit , 2, multiply by (-2), subtract this number(-4) from the number left which is 11-4=7.

Thus the number is divisible by 7

or 112--> 11-2x2 = 7 div by 7
296--> 29-6x2=21 div by 7

Divisibilty by 8--> Last 3 digits divisible by 8 or three or more zeros at the end.

Divisibility by 9--> Sum of digits divisible by 9

Divisibility by 10--> 0 at the end

Divisibility by 11--> Sum of digits at even and odd place are equal or differ by a number divisible by 11.

eg
3245682

Sum of digits at even place: 2+5+8=15
Sum of digits at odd place: 3+4+6+2=15

Their difference= 15-15=0, thus the number is divisible by 11

Divisibility by 12--> Number should be divisible by both 4 and 3
Divisibility by 13--> Remember a number +4, proceeding as in case of 7
Thus
143---> 14+3x4=26 ( div by 13)

Divisibility by 14--> Number should be divisible by both 2 and 7

Divisibility by 16--> Last 4 Digits divisible by 16

divisibility by 17--> Remember a number (-5) , proceed as in 7 and 13

1904= 190-4x5=170 (div by 17)

Divisibility by 18--> 9 and 2

Divisibility by 19--> Remember a number +2

342 = 34+2x2 = 38 (div by 19)