How to find if a number is divisible by 7? / Test of divisibility by 7: 

Following are the steps for divisibility by seven.

Step 1:  First, we have to take the last digit of the given number and double it.

Step 2:  After doubling it, you have to subtract the result from the remaining digits. 

Step 3:  You have to repeat this procedure until you find that the difference is divisible by 

             Seven or not. If the number is divisible by seven, then the original number will also 

             be divisible by seven.  

 Example 1: Which mental trick can be applied to determine whether the number 6902 is divisible by the number 7? 

Solution: Step 1:  We have to take the last digit of the number and we have to double it.

             The last digit you would notice is 2. If we double it will be (2*2=4)

Step 2:  After doubling it, we have to subtract it from the remaining digits.

             690 - 4 = 686.

Step 3:  Again, we have to repeat steps one and two.

             From 686 the last digit is 6. So, we will double it. (6 * 2=12)

             Subtract 12 from remaining digits i.e., 68

             68 - 12 = 56.  Since 56 is a multiple of seven, 6902 is divisible by 7. 

 Example 2: How divisibility test can be used to check if 4539 is divisible by seven? 

Solution: Step 1:  Take the last digit of the number and double it.

             The last digit is 9. So (9*2= 18) 

Step 2:  after doubling it we have to subtract it from the remaining digits 

              453 - 18 = 435 

Step 3:  we have to repeat steps one and two again

              From 435 the last digit is 5. After doubling it (5*2=10)

              43 - 10 = 42

              Since 42 is a multiple of seven. So, 4539 is divisible by seven. 

 How to find if a number is divisible by 10? / Test of divisibility by 10: 

To check the divisibility by 10, you have to check the last digit of a number. If the last digit of a number is zero then the entire number is divisible by 10. 

Example 3: Can the number 5690 be divtopicIded by the number 10? 

Solution: The last digit of the number 5690 is 0. So, the number 5690 turns out to be divisible by 10. 

 Example 4: Can you use the test of divisibility to find out whether the number 67809 is divisible by 10?  

Solution: The last digit of the number 67809 is nine. It is not zero. So, the number 67809 is not divisible by 10. 

 How to find if a number is divisible by 11? / Test of divisibility by 11: 

Following are the steps to check the divisibility by 11.

Step 1:  You have to find all the digits at the odd place and add them.

Step 2:  Next, you have to find all the digits at an even place and add them.

Step 3:  Find the difference between the sum of pain from step one and step two

Step 4:  If the difference is zero or multiple of 11, then it is divisible by 11. 

 Example 5: Is the five-digit number 79541 divisible by 11?

Solution: Step 1:  First you have to add all the digits at odd places

              7 + 5 + 1 = 13 

Step 2:   Next you have to add all the digits at even places.

              9 + 4 = 13 

Step 3:   Now we have to subtract the answers of step one and step two. 

              13 - 13 =0 

Step 4:   So, the difference between step 2 and step 3 is 30. Hence, 79541 is divisible by 11.