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Saturday, February 26, 2011

Divisibility tests of common numbers

Divisibility of different numbers has been listed below:

  • Divisibility by 2 : A number is divisible by 2, if its unit digits is any of 0,2,4,6,8.
    In other words, when the unit's place digit is even or zero (0).
  • Divisibility by 3 : A number is divisible by 3 only when the sum of its digits is divisible by 3. In other words,  All numbers with a digit sum of three (3), six (6) or nine (9) are divisible by 3.
  • Divisibility by 4 : A number is divisible by four (4), if its last two (2) digits are divisible by 4.
  • Divisibility by 5 : A number is divisible by 5 if its unit digit is five (5) or zero (0).
  • Divisibility by 6 : A number is divisible by 6 if it is divisible by both two (2) and three (3).
  • Divisibility by 8 : A number is divisible by eight (8) only when the number formed by its last three (3) digits is divisible by eight (8).
  • Divisibility by 9 : A number is divisible by nine (9) if sum of its digits is divisible by nine (9). In other words, All numbers with a digit sum is nine (9) are divisible by nine (9).
  • Divisibility by 10 : A number is divisible by ten (10) only when its unit digit is zero (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 zero (0) or number is divisible by 11.  In simple words,  Add all the digits in the ODD position and all digits in the EVEN position and subtract the smaller result from the larger result. If we get 0 or 11 or any multiples of 11 , then the number is divisible by 11.
    Example : 7352631
    Sum of odd digits : 7+5+6+1 = 19
    Sum of Even digits : 3+2+3 = 8
    19-8 = 11. So, number 7352631 is divisible by 11
  • Divisibility by 12 : A number is divisible by 12 if it is divisible by both three (3) and four (4).  In other words,  All numbers divisible by both 3 and 4 are divisible by 12.
  • Divisibility by 15 : A number is divisible by 15 if it is divisible by both three (3) and five (5).  In other words,  All numbers divisible by both 3 and 5 are divisible by 15.
  • Divisibility by 25 : A number is divisible by twenty-five (25) only when the number formed by its last two (2) digits is divisible by twenty-five (25).
  • Divisibility by 27 : A number is divisible by twenty-seven(27) if sum of its digits is divisible by twenty-seven(27).
  • Divisibility by 125 : A number is divisible by one hundred and twenty-five (125) only when the number formed by its last three (3) digits is divisible by one hundred and twenty-five (125).

An important note :  If a number N is divisible by two numbers m and n, where  m and n are co-primes(numbers having only 1 as a common factor or Two natural numbers a and b are said to be co-prime if their HCF(Highest Common Factor) is 1.), then N is divisible by mn.

Too err is human. If you see a typo, a spelling mistake, an error, or any other issue, please express via comments.

4 comments:

  1. Hi Bhai,
    Nice share. Can you please tell me what is a co-prime?

    ReplyDelete
  2. @riazresearch
    Numbers having only 1 as a common factor or Two natural numbers a and b are said to be co-prime if their HCF(Highest Common Factor) is 1. For Example (2,3), (4,5), (7,9), (8,11)etc. are pairs of co-primes. Because these have only 1 as the common factor.

    ReplyDelete
  3. great post buddy and this will be helping in quick calculation and will be saving much time.

    ReplyDelete
  4. Nice tips for divisibility.
    Through Vedic Maths one can find out the divisibility rule for 7 as well.
    www.vedicmathsindia.org

    ReplyDelete