Divisibility of numbers

Learning the criteria for divisibility by different numbers can come in handy when you have to solve difficult divisions problems. It is a very important tool that every student should learn and make use of this tool during calculations.

Divisibility of numbers

Let us learn the divisibility criteria of different numbers:

  • Divisibility by 2

Checking for divisibility by 2 is a very easy process. You simply need to check the last digit of the given number. If the last digit is an even number or 0, then the whole number is divisible by 2.

For example: 1)  986 – check for the last digit. The last digit is 6, which is an even number. Hence 986 is divisible by 2. 986/2 = 493.

2) 987 – check for the last digit. The last digit is 7, which is an odd number. Hence 987 is not divisible by 2.

  • Divisibility by 3

To check for divisibility of 3 add all digits of the number and divide that sum by 3. If the sum is divisible by 3, then the whole number will be divisible by 3.

For example: 1) Check whether 291 is divisible by 3. Add up all the digits of the number, .i.e, 2+9+1 =  12 . Now, we know that 12 is divisible by 3.

2) Check whether 457 is divisible by 3. Add up all the digits of the number.4+5+7 = 16.

We know that 16 is not divisible by 3. Hence, 457 is not divisible by 3.

  • Divisibility by 4

To check the divisibility of 4, check for the last two digits of the given number. If the number formed by the last two digits is divisible by 4, then the entire number will be divisible by 4.

For example: 1) Check if 8524 is divisible by 4. Now, the last two digits of this number are 24. We know that 24/4 = 6. So, we can be sure that 8524 is divisible by 4.                 8524/4 = 2131.

2) Check if 9904 is divisible by 4. Let us check for last two digits. The last two digits are 04, which is divisible by 4. Hence, 9904 is divisible by 4. 9904/4 = 2476

3) Check if 5643 is divisible by 4. 43 is not a multiple of 4. Hence 5643 will not be divisible by 4. 5643/4 = 1410 3/4.

  • Divisibility by 5

Divisibility rule for 5 is very simple. Any number, which ends with 0 or 5 is divisible by 5.

For example: 1) Check if 870 is divisible by 5.Since it ends with 0, it will be divisible by 5. 870/5 = 174.

2) Check if 195 is divisible by 5. Since it ends with 5, it will be divisible by 5. 195/5 = 39.

3) Check if 568 is divisible by 5. Since it doesn’t end with 0 or 5, it will not be divisible by 5.  Let us check for clarity. 568/5 = 113 3/5.

  • Divisibility by 6

To check for the divisibility of 6, you need to check if the number is divisible by 2 and 3. Only if the number is divisible by both 2 and 3, then the number will be divisible by 6. Let us learn this using example.

For example: Check if 576 is divisible by 6. Let us check if its divisible by 2 and 3:

  • 576 ends with the even number 6, hence its divisible by 2.
  • The sum of the digits; 5+7+6 = 18; and 18 is divisible by 3.
  • Hence, 576 should be divisible by 6. 576/6 = 96.
  • Divisibility by 7

To check for the divisibility of 7, follow these steps:

  1. Remove the last digit of the number given.
  2. Double this digit.
  3. Subtract this doubled digit from the number obtained in step 1.
  4. Now check, if the difference obtained is divisible by 7. If this difference is also a big number, follow the same steps as before, until you get a small number that is divisible by 7.

For example:  Check whether 294 is divisible by 7. To check this, remove the last digit from the number.i.e. 4. Now the number becomes 29. Double the digit removed, i.e., 4. 4*2 = 8. And , now subtract 8 from 29 .  29-8=21. Now , we know that 21 is divisible by 7 . 21/7 = 3. Hence , we can confirm that 294 is divisible by 7.

  • Divisibility by 8

To check the divisibility of 8 , simply check the last 3 digits of the number . If the number formed by the last 3 digits is divisible by 8 , then the whole number is divisible by 8.

For example : Take the number 6328 . To check its divisibility by 8 , take the last 3 digits i.e., 328. Now 328 is divisible by 8 and 328/8 = 41.  So, the number 6328 is divisible by 8. And , 6328/8 = 791.

  • Divisibility by 9

To check for divisibility of 9 , add all digits of the number , and divide that sum by 9. If the sum is divisible by 9 , then the whole number will be divisible by 9 .

For example : Take the number 468 . Now add all the digits , 4+6+8 = 18. Now , we know that 18 is divisible by 9. Hence , 468 will be divisible by 9. 468/9 = 52.

  • Divisibility by 10

All the numbers that end in 0 , are divisible by 10.

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Practise This Question

The de Broglie wavelength of a particle with mass 1 gram and velocity 100 m/sec is