Divisibility Shortcut Tricks - Basic Math Tricks Part 4

Basic Tricks - PART-4

Divisibility Shortcut Tricks

Divisibility Rules

• If the end digit of any number is Zero or Even Number then number can easily Divisible by 2. Example: 4587952/2 = 2293976.

• If the Sum of all numbers is divisible by 3 then the number is divisible by 3. Example:(8+6+1) = 15 and 15 is divisible by 3, So the 861 is divisible by 3. Some more Example: 22104/3 = 7368. (2+2+1+0+4) = 9. 9/3 = 3, So 22104 divisible by 3.

• The number is Divisible by 4 when the end of two digit is divisible by 4 or end of two digit is Zero. Example: 85736 = 21434. (End two digit divisible by 4). 98300 = 24575 (End of both digit is Zero).

• The number is end with Zero or 5 Then the number is divisible by 5. Example: 7775/5 = 1555 (End digit is 5), 3390/5 = 678 (End digit is 0).

• The number is divisible by 6 when the number is divisible by 3 and 2. So both the condition should be satisfied by Rule 3 and 2 otherwise number will be not divisible by 6. 5844/6 = 974 (Both condition are satisfied).

•  Three end digit of number if divisible by 8 and if the last three digit is Zero then the number is also divisible by 8. Example:224256/8=28032 here the last digit 256 is divisible by 8 so the total number should be divisible by 8. 92045000/8=11505625.last three digit is Zero so the number is divisible by 8.

• All digits sum of a number if divisible by 9 then the number is divisible by 9. Example: 9522:(9+5+2+2)=18 that is divisible by 9 so the number 9522/9=1058.

• The number is divisible by 10 if the number is end with Zero then the number divisible by 10. Example: 4790/10=479 and 1250/10=125 this two numbers are end with Zero that why it is divisible by 10.

• Using 11 a number is divisible if difference sum of Even places and sum of odd places is Zero so divisible by 11. Example: 1236431460/11=112402860. (1+3+4+1+6)(odd places)-(2+6+3+4+0)(Even places)=0 and sum of odd and Even digit is equal so the number is divisible by 11.

• We can write 15 as (5×3) so if a number is divisible by 5 and 3 then the number is divisible by 15.

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Shortcut to divide any 2 digit number by 5

Using this shortcut method to divide, You can divide any 2 digit number by 5 within seconds.

Let us see the steps on how to divide any number by 5

Step 1:Double the given number.

Step 2:Shift the decimal point to the left by one place.

Now we shall practice some examples using this trick

Example 1:  42/5=?

Step 1:By doubling 42 we get 84.

Step 2:By shifting the decimal point to the left by one place we get 8.4

Ans  42/5=8.4

Example 2: 18/5=?

Step 1:By doubling 18 we get 36.

Step 2:By shifting the decimal point to the left by one place we get 3.6

Ans  18/5=3.6

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Shortcut to divide any 2 digit number by 9

Dividing a two digit number by 9 using the method taught to us in our school days may take a minute. But by applying this trick you can mentally calculate the answer within seconds.

Let us see the steps now

Step 1: Enter the ten’s digit of the number as it is.

Step 2: To get the unit’s place digit add the ten’s place digit number and Unit’s place digit number and put the decimal point after the ten’s place digit.

Let us consider an example

Example: 23÷ 9=?

Step 1: We enter the ten’s place digit as it is

            Ten’s place digit=2

Step 2: We get the unit’s place digit by adding ten’s place digit and unit’s place digit

            2+3=5

            Unit’s place digit=5

Now add a decimal point between the unit’s place digit and the ten’s place digit to arrive at the answer

Ans  : 23÷ 9 =2.5

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Divisibility of a number by 2 shortcut tricks

Divisibility of a number by 2
If the end digit of any number is Zero or Even Number then number than it can easily Divisible by 2.

Example: 88888 / 2 = 44444

Example: 4587952 / 2 = 2293976

Example: 22334488 / 2 = 11167244

Example: 3987284 / 2 = 1993642

Example: 25873252 = 12936626

Example: 2458 / 2 = 1229

Note: All this numbers are divisible by 2 because of end digit from right side is even that’s why the number is divisible by 2 , 1235643 , 125787 , 4587121 and this numbers are not divisible by 2 because the end digit is odd number.

Example: 39872840 / 2 = 19936420

Example: 223344880 / 2 = 111672440

Example: 258732520 / 2 =129366260

Example: 888880 / 2 = 444440

Example: 24580 / 2 = 12290

Note: All this numbers are divisible by 2 because of end digit from right side is Zero that’s why the number is divisible by 2 .

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Divisibility of a number by 3 shortcut tricks

Divisibility of a number by 3

If the Sum or addition of all numbers that is given is divisible by 3 then the number is divisible by 3.

Example: 861 / 3 = 287. (8+6+1) = 15 and 15 is divisible by 3, So the 861 is divisible by 3.

Example: 22104 / 3 = 7368. (2+2+1+0+4) = 9. 9 / 3 = 3, So 22104 divisible by 3.

Example: 99954 / 3 = 33318. (9+9+9+5+4) = 36. 36 / 3 = 12, So 99954 divisible by 3

Example: 87921 / 3 = 29307. (8+7+9+2+1) = 27. 27 / 3 = 9, So 87921 divisible by 3

Example: 69321 / 3 = 23107. (6+9+3+2+1) = 21. 21 / 3 = 7, So 69321 divisible by 3

Example: 1359 / 3 = 453. (1+3+5+9) = 18. 18 / 3 = 6, So 1359 divisible by 3

Note: So Before going to divisible by 3 any number, first check the addition of all numbers is divisible by 3.

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Divisibility of a number by 4 shortcut tricks

Divisibility of a number by 4

The number is Divisible by 4 when the end of two digit from right end is divisible by 4 or end of two digit is Zero.

Example: 85736 = 21434. (End two digit divisible by 4).So the number is divisible by 4.

Example: 58648 / 4 = 14662. (End two digit divisible by 4).So the number is divisible by 4.

Example: 85728 / 4 = 21432. (End two digit divisible by 4).So the number is divisible by 4.

Example: 3571916 / 4 = 892979. (End two digit divisible by 4).So the number is divisible by 4.

Example: 4781204 / 4 = 119530. (End two digit divisible by 4).So the number is divisible by 4.

Note: The number is divisible by 4 if the end of two digit from right end is Zero.

Example: 98300 = 24575 (End of both digit is Zero).So the number is divisible by 4.

Example: 8573600 = 2143400.(End of both digit is Zero).So the number is divisible by 4.

Example: 5864800 / 4 = 1466200.(End of both digit is Zero).So the number is divisible by 4.

Example: 8572800 / 4 = 2143200.(End of both digit is Zero).So the number is divisible by 4.

Example: 357191600 / 4 = 89297900.(End of both digit is Zero).So the number is divisible by 4.

Example: 478120400 / 4 = 119530100.(End of both digit is Zero).So the number is divisible by 4.

Note: So Before going to divisible by 4 any number, first check the end of two digit is from right end is divisible by 4 or end of two digit is Zero.Than all numbers is divisible by 4.

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Divisibility of a number by 5 shortcut tricks

Divisibility of a number by 5 shortcut tricks

The number is Divisible by 5 when the number is end with Zero or 5 Then the number is divisible by 5.

Example: 7775/5 = 1555 (End digit is 5).

Example: 3395 / 5 = 679 (End digit is 5).

Example: 45865 / 5 = 9173 (End digit is 5).

Example: 357555 / 5 = 71511 (End digit is 5).

Example: 3398795 / 5 = 679759 (End digit is 5).

Example: 33945785 / 5 = 6789157 (End digit is 5).

Example: 339456795 / 5 = 67891359 (End digit is 5).

Example: 3395254785 / 5 = 679050957 (End digit is 5).

Note: The number is divisible by 5 if the end of one digit from right end is Zero.

Example: 33950/5 = 6790 (End digit is 5).

Example: 458650 / 5 = 91730(End digit is 0).

Example: 3575550 / 5 = 715110 (End digit is 0).

Example: 33987950 / 5 = 6797590 (End digit is 0).

Example: 339457850 / 5 = 67891570 (End digit is 0).

Example: 3394567950 / 5 = 678913590 (End digit is 0).

Example: 33952547850 / 5 = 6790509570 (End digit is 0).

Note: So Before going to divisible by 5 any number, first check the end of one digit is from right end is 5 or end of one digit is Zero.Than all numbers is divisible by 5.

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Divisibility of a number by 6 shortcut tricks

Divisibility of a number by 6 shortcut tricks

The number is divisible by 6 when the number is divisible by 3 and 2. So both the condition should be satisfied by Rule 3 and 2 otherwise number will be not divisible by 6.

Example: 5844 / 6 = 974 (Both condition are satisfied).

Example: 76422 / 6 = 12737 (Both condition are satisfied).

Example: 723294 / 6 = 120549 (Both condition are satisfied).

Example: 7858446 / 6 = 1309741 (Both condition are satisfied).

Example: 38443692 / 6 = 6407282 (Both condition are satisfied).

Example: 547121844 / 6 = 91186974 (Both condition are satisfied).

Example: 5862359442 / 6 = 977059907 (Both condition are satisfied).

Example: 58652570982 / 6 = 9775428497 (Both condition are satisfied).

Example: 584396125734 / 6 = 97399354289 (Both condition are satisfied).

Note: So Before going to divisible by 6 any number, first check the condition of 2 and 3 are satisfied.Than all numbers is divisible by 6.

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Divisibility of a number by 8 shortcut tricks

Divisibility of a number by 8 shortcut tricks :

Three end digit of a number if divisible by 8 and last three digit is Zero  then the number is  divisible by 8.

Example: 65415624000/8=8176953000. last three digit is Zero so the number is divisible by 8.

Example: 32562984000/8=4070373000. last three digit is Zero so the number is divisible by 8.

Example: 224256/8=28032 . last digit 256 is divisible by 8 so the total number should be divisible by 8.

Example: 46045392000/8=5755674000. last three digit is Zero so the number is divisible by 8.

Example: 46045392/8=5755674. last three digit number Divisible by 8.so the number is divisible by 8.

Example: 2879632000/8=359954000. last three digit is Zero so the number is divisible by 8.

Example: 33399944000/8=4174993000. last three digit is Zero so the number is divisible by 8.

Example: 65415624/8=8176953. last three digit number Divisible by 8.so the number is divisible by 8.

Example: 28796320/8=3599540. last three digit number Divisible by 8.so the number is divisible by 8.

Example: 32562984/8=4070373. last three digit number Divisible by 8.so the number is divisible by 8.

Example: 33399944/8=4174993. last three digit number Divisible by 8.so the number is divisible by 8.

Note: So Before going to divisible by 8 any number, first check the condition of last three digit is divisible by 8 or last three digit is Zero.Than all numbers is divisible by 8.

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Divisibility of a number by 9 shortcut tricks

Divisibility of a number by 9 shortcut tricks

All digits sum of a number if divisible by 9 then the number is divisible by 9.

Example: 9981: (9+9+8+1)=27 that is divisible by 9 so the number 9981/9 = 1109.

Example: 89874: (8+9+8+7+4)=36 that is divisible by 9 so the number 89874/9 = 9986.

Example: 9522: (9+5+2+2)=18 that is divisible by 9 so the number 9522/9 = 1058.

Example: 499869: (4+9+9+8+6+9) = 45 that is divisible by 9 so the number 499869/9 = 55541.

Example: 77896593: (7+7+8+9+6+5+9+3) = 54 that is divisible by 9 so the number 77896593/9 = 8655177.

Example: 778965939: (7+7+8+9+6+5+9+3+9) = 63 that is divisible by 9 so the number 778965939/9 = 1086551771.

Example: 999988875: (9+9+9+9+8+8+8+7+5) = 72 that is divisible by 9 so the number 999988875/9 = 111109875.

Example: 33778899999: (3+3+7+7+8+8+9+9+9+9) = 81 that is divisible by 9 so the number 33778899999/9 = 3753211111.

Example: 99999888876: (9+5+2+2) = 90 that is divisible by 9 so the number 99999888876/9 = 11111098764.

Example: 19873895896989: (1+9+8+7+3+8+9+5+8+9+6+9+8+9) =99 that is divisible by 9 so the number 19873895896989/9 = 2208210655221.

Note: So Before going to divisible by 9 any number, first check the condition of  All digit sum is divisible by 9 .Than numbers is divisible by 9.

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Divisibility of a number by 10 shortcut tricks

Divisibility of a number by 10 shortcut tricks

The number is divisible by 10 if the number is end with Zero then the number divisible by 10.

Example: 4790/10 = 479 The numbers are end with Zero that why it is divisible by 10.

Example: 1250/10 = 125 The numbers are end with Zero that why it is divisible by 10.

Example: 336650/10 = 33665 The numbers are end with Zero that why it is divisible by 10.

Example: 2563140/10 = 256314 The numbers are end with Zero that why it is divisible by 10.

Example: 14587930/10= 1458793 The numbers are end with Zero that why it is divisible by 10.

Example: 587985460/10= 58798546 The numbers are end with Zero that why it is divisible by 10.

Example: 85264768510/10= 8526476851 The numbers are end with Zero that why it is divisible by 10.

Example: 215487896310/10= 21548789631 The numbers are end with Zero that why it is divisible by 10.

Example: 4587921545950/10= 458792154595 The numbers are end with Zero that why it is divisible by 10.

Note: So Before going to divisible by 10 any number, first check the condition of end with Single Zero digit is divisible by 10 .Than numbers is divisible by 10.

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Divisibility of a number by 11 shortcut tricks

Divisibility of a number by 11 shortcut tricks

Using 11 a number is divisible if difference sum of Even places and sum of odd places is Zero so divisible by 11.

Example: 1236431460/11= 112402860. (1+3+4+1+6)(odd places)-(2+6+3+4+0)(Even places)=0 andsum of odd and Even digit is equal so the number is divisible by 11.

Example: 513678/11= 46698.(5+3+7)(odd places)-(1+6+8)(Even places)=0 and sum of odd and Even digit is equal so the number is divisible by 11.

Example: 874720/11= 79520. (8+4+2)(odd places)-(7+7+0)(Even places)=0 and sum of odd and Even digit is equal so the number is divisible by 11.

Example: 697972/11= 63452. (6+7+7)(odd places)-(9+9+2)(Even places)=0 and sum of odd and Even digit is equal so the number is divisible by 11.

Example: 7972813805/11= 724801255. (7+7+8+3+0)(odd places)-(9+2+1+8+5)(Even places)=0 andsum of odd and Even digit is equal so the number is divisible by 11.

Note: So Before going to divisible by 10 any number, first check the condition of sum of odd and Even digit is equal and difference sum of Even places and sum of odd places is Zero is divisible by 10 .Than numbers is divisible by 10.

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Divisibility of a number by 15 shortcut tricks

Divisibility of a number by 15 shortcut tricks

We can write 15 as (5×3) so if a number is divisible by 5 and 3 then the number is divisible by 15.

Example: 75 / 15= 5 because 75 is divisible by 5 and 3 .so the number is divisible by 15.

Example: 35445 / 15= 2363 because 75 is divisible by 5 and 3 .so the number is divisible by 15.

Example: 756555 / 15= 50437 because 75 is divisible by 5 and 3 .so the number is divisible by 15.

Example: 2034645 / 15= 135643 because 75 is divisible by 5 and 3 .so the number is divisible by 15.

Example: 59985465 / 15= 3999031because 75 is divisible by 5 and 3 .so the number is divisible by 15.

Note: So Before going to divisible by 15 any number, first check the condition of a number isdivisible by 5 and 3 is possible than divisible by 15 is possible. Than numbers is divisible by 15.