Which of the following numbers are divisible by 3 or 9:

(i) 7341

(ii) 59031

(iii) 12345678

(iv) 560319

(v) 720634

(vi) 3721509

A number is divisible by 3 if the sum of its digits is divisible by 3.

A number is divisible by 9 if the sum of its digits is divisible by 9.

(i) 7341 — sum of digits = 7 + 3 + 4 + 1 = 15.

15 is divisible by 3 but not by 9.

Hence, 7341 is divisible by 3 only.

(ii) 59031 — sum of digits = 5 + 9 + 0 + 3 + 1 = 18.

18 is divisible by both 3 and 9.

Hence, 59031 is divisible by both 3 and 9.

(iii) 12345678 — sum of digits = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 = 36.

36 is divisible by both 3 and 9.

Hence, 12345678 is divisible by both 3 and 9.

(iv) 560319 — sum of digits = 5 + 6 + 0 + 3 + 1 + 9 = 24.

24 is divisible by 3 but not by 9.

Hence, 560319 is divisible by 3 only.

(v) 720634 — sum of digits = 7 + 2 + 0 + 6 + 3 + 4 = 22.

22 is not divisible by 3.

Hence, 720634 is not divisible by 3 or 9.

(vi) 3721509 — sum of digits = 3 + 7 + 2 + 1 + 5 + 0 + 9 = 27.

27 is divisible by both 3 and 9.

Hence, 3721509 is divisible by both 3 and 9.