Question

Test the divisibility of each of the following numers by 3:
(i) 83
(ii) 378
(iii) 474
(iv) 1693
(v) 20345
(vi) 67035
(vii) 591282
(viii) 903164
(ix) 100002

Answer 1

A given number is divisible by 3 only when the sum of its digits is divisible by 3.

(i) 83
The sum of the digits is 8 + 3 = 11 which is not divisible by 3. So, 83 is not divisible by 3.

(ii) 378
The sum of the digits is 3 + 7 + 8 = 18 which is divisible by 3. So, 378 is divisible by 3.

(iii) 474
The sum of the digits is 4 + 7 + 4 = 15 which is divisible by 3. So, 474 is divisible by 3.

(iv) 1693
The sum of the digits is 1 + 6 + 9 + 3 = 19 which is not divisible by 3. So, 1693 is not divisible by 3.

(v) 20345
The sum of the digits is 2 + 0 + 3 + 4 + 5 = 14 which is not divisible by 3. So, 20345 is not divisible by 3.

(vi) 67035
The sum of the digits is 6 + 7 + 0 + 3 + 5 = 21 which is divisible by 3. So, 67035 is divisible by 3.

(vii) 591282
The sum of the digits is 5 + 9 + 1 + 2 + 8 + 2 = 27 which is divisible by 3. So, 591282 is divisible by 3.

(viii) 903164
The sum of the digits is 9 + 0 + 3 + 1 + 6 + 4 = 23 which is not divisible by 3. So, 903164 is not divisible by 3.

(ix) 100002
The sum of the digits is 1 + 0 + 0 + 0 + 0 + 2 = 3 which is divisible by 3. So, 100002 is divisible by 3.