{"id":757,"date":"2020-10-02T01:46:01","date_gmt":"2020-10-02T01:46:01","guid":{"rendered":"http:\/\/themindpalace.in\/?p=757"},"modified":"2021-08-28T09:39:49","modified_gmt":"2021-08-28T09:39:49","slug":"divisibility-rule","status":"publish","type":"post","link":"https:\/\/themindpalace.in\/index.php\/2020\/10\/02\/divisibility-rule\/","title":{"rendered":"Playing with Numbers Part-2 Divisibility Rule."},"content":{"rendered":"\n

Summary of playing with numbers part2<\/a><\/p>\n\n\n\n

Solved exercise of playing with numbers<\/a><\/p>\n\n\n\n

\"\"<\/figure><\/div>\n\n\n\n

Summary<\/h1>\n\n\n\n

It help us to check from which number the number is divisible without actually dividing.<\/p>\n\n\n\n

An integer a and integer b not equal to zero and there exist an integer c, such that AC is equal to b.we write a divided by b to indicate that a divides b *divisibility is a positive property.<\/p>\n\n\n\n

Divisibility Rule for 2<\/span><\/strong><\/h4>\n\n\n\n

A number is divisible by 2 if the one\u2019s digit is even. Therefore, any number that ends with 0,2,4,6, or 8 is divisible by 2.<\/p>\n\n\n\n

Example: 62,108,63564,70006….<\/span><\/p>\n\n\n\n

Divisibility Rule for 3<\/span><\/strong><\/h4>\n\n\n\n

A number is divisible by 3 if the sum of the digits is divisible by 3 <\/p>\n\n\n\n

Example:96 we have to add the digit 9+6=15<\/span><\/p>\n\n\n\n

15 is a multiple of 3, therefore 96 is divisible by 3.<\/p>\n\n\n\n

Divisibility rule for 4<\/span><\/strong><\/h4>\n\n\n\n

A number is divisible by 4 if the number formed by the last two digits is divisible by 4.<\/p>\n\n\n\n

Example: 124 last two digits in 124 or 24, 24 is multiple of 4 therefore 124 is divisible by 4.<\/span><\/p>\n\n\n\n

Divisibility rule for 5<\/span><\/h4>\n\n\n\n

A number is divisible by 5 if the last digit is 0 or 5.<\/p>\n\n\n\n

Example: 100, 455, 680….<\/span><\/p>\n\n\n\n

Divisibility rule for 6<\/span><\/strong><\/h4>\n\n\n\n

A number is divisible by 6 if it is divisible by 2, 3.<\/p>\n\n\n\n

Lets look at the number 132<\/p>\n\n\n\n

  • 132 is an even number.<\/li>
  • And, sum of the digits is 1 + 3 + 2=6<\/li>
  • 6 is a multiple of 3, therefore 132 is divisible by 6.<\/li><\/ul>\n\n\n\n

    Divisibility rule for 7<\/span><\/strong><\/h4>\n\n\n\n

    we check whether the number is divisible by 7 by following the given steps, take the last digit of the number double it subtract the doubled number from the remaining number* if the result is divisible by 7 ,then the number is divisible by 7.<\/p>\n\n\n\n

    Example: 203<\/span><\/p>\n\n\n\n

    • The last digit of 203 is 3<\/li>
    • Double of 3 =3 X 2 = 6<\/li>
    • Subtract 6 from 20, 20 \u2013 6 = 14<\/li>
    • 14 is multiple of 7 then the number 203 is divisible by 7<\/li><\/ul>\n\n\n\n

      Divisibility rule for 8<\/span><\/strong><\/h4>\n\n\n\n

      A number is divisible by 8 if the last three digits divisible by 8<\/p>\n\n\n\n

      Example: 9640<\/span><\/p>\n\n\n\n

      640 \u00f7 8 = 80 it\u2019s a multiple of 8<\/p>\n\n\n\n

      Therefore 9640, is divisible by 8<\/p>\n\n\n\n

      Divisibility rule for 9<\/span><\/strong><\/h4>\n\n\n\n

      A number is divisible by 9, if the sum of the digits of the number is divisible by 9.<\/p>\n\n\n\n

      Examples: 3573 = 3 + 5 + 7 + 3 = 18<\/span><\/p>\n\n\n\n

      18 is a multiple of 9 therefore 3573 is divisible by 9<\/p>\n\n\n\n

      Divisibility rule for 10<\/span><\/strong><\/h4>\n\n\n\n

      A number is divisible by 10 if the number\u2019s  units place is 0.<\/p>\n\n\n\n

      Examples: 35680 is divisible 10 because its one\u2019s place is 0<\/span><\/p>\n\n\n\n

      Divisibility rule for 11<\/span><\/strong><\/h4>\n\n\n\n

      According to the divisibility rule of 11, we must subtract.The steps followed are, add the digits in odd places, add the digits in even place, find the difference between both of them. If answer is either zero or divisible by 11, then it is divisible.<\/p>\n\n\n\n

      Example:   1353<\/span><\/p>\n\n\n\n

      [1 + 5] \u2013 [ 3+3] = 6 -6 = 0 therefore the number is divisible by 11.<\/p>\n\n\n\n

      Odd an Even places<\/span><\/h4>\n\n\n\n

      Divisibility Rule for 12<\/span><\/h4>\n\n\n\n

      A number is divisible by 12 if it is divisible by both 3 and 4.<\/p>\n\n\n\n

      Example: 384 is divisible by 12.<\/span><\/p>\n\n\n\n

      3 + 8 + 4= 15 it\u2019s a multiple of 3,<\/p>\n\n\n\n

      84 is divisible by 4 therefore the number 384 is divisible by 12.<\/p>\n\n\n\n

      \n