Test the divisibility of each of the following numbers by 7:

Solution:

(i) 693

69 − (2 × 3) = 69 − 6 = 63, which is divisible by 7.

Hence, 693 is divisible by 7.

(ii) 7896

789 − (2 × 6) = 789 − 12 = 777, which is divisible by 7.

Hence, 7896 is divisible by 7.

(iii) 3467

346 − (2 × 7) = 346 − 14 = 332, which is not divisible by 7.

Hence, 3467 is not divisible by 7.

(iv) 12873

1287 − (2 × 3) = 1287 − 6 = 1281, which is divisible by 7.

Hence, 12873 is divisible by 7.

(v) 65436

6543 − (2 × 6) = 6543 − 12 = 6531, which is divisible by 7.

Hence, 65436 is divisible by 7.

(vi) 54636

5463 − (2 × 6) = 5463 − 12 = 5451, which is not divisible by 7.

Hence, 54636 is not divisible by 7.

(vii) 98175

9817 − (2 × 5) = 9817 − 10 = 9807, which is divisible by 7.

Hence, 98175 is divisible by 7.

(viii) 88777

8877 − (2 × 7) = 8877 − 14 = 8863, which is not divisible by 7.

Hence, 88777 is not divisible by 7.