(i) 65436
We know that if number formed by removing last digit is subtracted by double of removed digit, is divisible by 7, then our given number is divisible by 7.
Here last digit is 6.
∴ Number to be tested = 6543 – 2 × 6 = 6531.
Again repeating the process, taking last digit 1 for number 6531,
Number to be tested = 653 – 2 × 1 = 651
Again repeating the process, taking last digit 1 for number 651,
Number to be tested = 65 – 2 × 1 = 63, which is divisible by 7.
Hence, 65436 is divisible by 7.
(ii) 54636
We know that if number formed by removing last digit is subtracted by double of removed digit, is divisible by 7, then our given number is divisible by 7.
Here last digit is 6.
∴ Number to be tested = 5463 – 2 × 6 = 5451
Again repeating the process, taking last digit 1 for number 5451,
Number to be tested = 545 – 2 × 1 = 543
Again repeating the process, taking last digit 3 for number 543,
Number to be tested = 54 – 2 × 3 = 48, which is not divisible by 7.
Hence, 54636 is not divisible by 7.
(iii) 98175
We know that if number formed by removing last digit is subtracted by double of removed digit, is divisible by 7, then our given number is divisible by 7.
Here last digit is 5.
∴ Number to be tested = 9817 – 2 × 5 = 9807.
Again repeating the process, taking last digit 7 for number 9807,
Number to be tested = 980 – 2 × 7 = 966
Again repeating the process, taking last digit 6 for number 966,
Number to be tested = 96 – 2 × 6 = 84, which is divisible by 7.
Hence, 98175 is divisible by 7.
(iv) 88777
We know that if number formed by removing last digit is subtracted by double of removed digit, is divisible by 7, then our given number is divisible by 7.
Here last digit is 7.
∴ Number to be tested = 8877 – 2 × 7 = 8863.
Again repeating the process, taking last digit 3 for number 8863,
Number to be tested = 886 – 2 × 3 = 880
Here, last digit is 0. So, last digit will not be considered.
Hence, our number testing number will be 88, which is not divisible by 7.
Hence, 88777 is not divisible by 7.
