Chap 16 PLAYING WITH NUMBERS

Chap 16

PLAYING WITH NUMBERS

SOME IMPORTANT FACTS

1.      ab is two digit number and ab = 10 a  + b

2.      ab + ba  = 11 ( a + b ) , i.e. ab + ba is divisible by 11.

3.      i)          if   a = b , then ab – ba = 0

i)                    if   b >  a , then ba – ab  = 9 ( b – a ), i.e. ba – ab is divisible by 9.

ii)                  If  a > b , then ab – ba  = 9 ( b – a ), ie.  ab – ba is divisible by 9.

4.      abc is three digit number and abc = 100a + 10 b + c .

5.      i)          if a > c, then abc – cba = 99 ( a – c )

i)                    if c > a, then cba – abc = 99 ( c – a )

ii)                  if a = c , then abc – cba = 0

iii)   Tests for Divisibility

Divisibility Tests	Example
A number is divisible by 2  if the last digit is 0, 2, 4, 6 or 8.	178 is divisible by 2 since the last digit is 8.
A number is divisible by 3  if the sum of the digits is divisible by 3.	138 is divisible by 3 since the sum of the digits is 15 (1+3+8=12), and 12 is divisible by 3.
A number is divisible by 4  if the number formed by the last two digits is divisible by 4.	312 is divisible by 4 since 12 is divisible by 4.
A number is divisible by 5  if the last digit is either 0 or 5.	295 is divisible by 5 since the last digit is 5.
A number is divisible by 6  if it is divisible by 2 and it is divisible by 3.	168 is divisible by 6 since it is divisible by 2  and it is divisible by 3.
A number is divisible by 8  if the number formed by the last three digits is divisible by 8.	8,120 is divisible by 8 since 120 is divisible by 8.
A number is divisible by 9  if the sum of the digits is divisible by 9.	540 is divisible by 9 since the sum of the digits is 18 (5+4+0=9), and 9 is divisible by 9.
A number is divisible by 10  if the last digit is 0.	1,370 is divisible by 10 since the last digit is 0.

Test for 11 ; 

a)         A 2 digit number is divisible by 11 if its two digits are equal

b)         A 3 digit number is divisible by 11 if the sum of its outer two digits minus

its middle digit is a multiple of 11.

 c)        In general , if the difference of the sum of its digits in odd places and sum of its digits in even places ( starting from ones place ) is either 0 or divisible by 11.