(i) 693
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 3.
∴ Number to be tested = 69 – 2 × 3 = 63, which is divisible by 7.
Hence, 693 is divisible by 7.
(ii) 7896
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 = 789 – 2 × 6 = 777, which is divisible by 7.
Hence, 7896 is divisible by 7.
(iii) 3467
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 = 346 – 2 × 7 = 332.
Again repeating the process, taking last digit 2 for number 332,
Number to be tested = 33 – 2 × 4 = 19, which is not divisible by 7.
Hence, 3467 is not divisible by 7.
(iv) 12873
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 3.
∴ Number to be tested = 1287 – 2 × 3 = 1281.
Again repeating the process, taking last digit 1 for number 1281,
Number to be tested = 128 – 2 × 1 = 126, which is divisible by 7.
Hence, 12873 is divisible by 7.
