Xxxa is divisible by 9, what is the least natural no at a?
Answers
Answer:
Least natural no at a is 3
Step-by-step explanation:
We are given that xxxa is divisible by 9
To find: least natural no at a
Divisibility rule of 9 states that if sum of digits of no. is divisible by 9 then no. is divisible by 9.
Since x & a are digits, It only takes value from 0 - 9
Case 1,
when x = 1
we have 111a
sum of digits = 1 + 1 + 1 + a = 3 + a
3 + a is divisible by 9
⇒ a = 6
Case 2,
when x = 2
we have 222a
sum of digits = 2 + 2 + 2 + a = 6 + a
6 + a is divisible by 9
⇒ a = 3
Case 3,
when x = 3
we have 333a
sum of digits = 9 + a
9 + a is divisible by 9
⇒ a = 0
Case 4,
when x = 4
we have 444a
sum of digits = 12 + a
12 + a is divisible by 9
⇒ a = 6
Case 5,
when x = 5
we have 555a
sum of digits = 15 + a
15 + a is divisible by 9
⇒ a = 3
Case 6,
when x = 6
we have 666a
sum of digits = 18 + a
18 + a is divisible by 9
⇒ a = 0
Case 7,
when x = 7
we have 777a
sum of digits = 21 + a
21 + a is divisible by 9
⇒ a = 6
Case 8,
when x = 8
we have 888a
sum of digits = 24 + a
24 + a is divisible by 9
⇒ a = 3
Case 9,
when x = 9
we have 999a
sum of digits = 27 + a
27 + a is divisible by 9
⇒ a = 0
Therefore, Least natural no at a is 3