Question

Which of the following numbers are divisible by 3?
(i) 83
(ii) 78
(iii) 474
(iv) 1693
(v) 267144
(vi) 372416
(vii) 1248965
(viii) 9412503

Answer 1

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

(i) 83
Sum of its digits = 8 + 3 = 11
11 is not divisible by 3.
So, 83 is not divisible by 3

(ii) 78
Sum of its digits = 7 + 8 = 15
15 is divisible by 3.
So, 78 is divisible by 3.

(iii) 474
Sum of its digits = 4+7+4 = 15
15 is divisible by 3.
So, 474 is divisible by 3.

(iv) 1693
Sum of its digits = 1+6+9+3 = 19
19 is not divisible by 3.
So, 1693 is not divisible by 3.

(v) 267144
Sum of its digits = 2+6+7+1+4+4=24
24 is divisible by 3.
So, 267144 is divisible by 3.

(vi) 372416
Sum of its digits = 3+7+2+4+1+6=23
23 is not divisible by 3.
So, 372416 is not divisible by 3.

(vii) 1248965
Sum of its digits = 1+2+4+8+9+6+5=35
35 is not divisible by 3.
So, 1248965 is not divisible by 3.

(viii) 9412503
Sum of its digits = 9+4+1+2+5+0+3=24
24 is divisible by 3.
So, 9412503 is divisible by 3.