Steps to simplify the numbers


TESTS OF DIVISIBILITY[ Chapter #1]

1. Divisibility By 2:
             A number is divisible by 2 if its unit digit is any of [0,2,4,6,8]
   Example:
  • 3468 is divisible by 2 while 86945 is not divisible by 2

2. Divisibility By 3:
             A number is divisible by 3 only when the sum of its digits is divisible by 3.
Example:
  •    In the number 345, the sum of digits[3+4+5=12] which is divisible by 3
  •    In the number 445, the sum of digits[4+4+5=13] which is not divisible by 3            
3. Divisibility By 9:
               A number is divisible by 9 only when the sum of its digits is divisible by 9.
Example:
  • In the number 246591, the sum of digits[2+4+6+5+9+1=27] which is divisible by 9
4. Divisibility By 8:
                A number is divisible by 8 if the number formed by hundred's ten's and unit's digit of the given number is divisible by 8.
Example:
  • In the number 16789352, the number formed by last 3 digits namely 352 is divisible by 8.
So 16789352 is divisible by 8.

5. Divisibility By 10:
           A number is divisible by 10 only when its unit digit is 0
Example:

  • 7560 is divisible by 10 since its unit digit is 0
  • 67805 is not divisible by 10 since its unit digit is 5
6. Divisibility By 5:

            A number is divisible by 5 only when its unit digit is 0 or 5.
Example:
  • 58595 and 30055 is divisible by 5
7. Divisibility By 4:
          A number is divisible by 4 is the sum of its last two digits is divisible by 4.
Example:
  • 6879376 is divisible by 4 since 76 is divisible by 4
8. Divisibility By 11:
          A number is divisible by 11 if the difference between 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.
Example:
  • Consider the number  29435417
  • [Sum of its digits @ odd places]-[ Sum of its digits @ even places]
  • =[7+4+3+9]-[1+5+4+2]=11 which is divisible by 11
Therefore 29435417 is divisible by 11.