Question

What is the least number of digits in the number formed from only zeroes and ones such that the number is divisible by 225?
1. 4
2. 9
3. 11
4. 7​

Answer 1

What is the least number of digits in the number formed from only zeroes and ones such that the number is divisible by 225?

1. 4
2. 9
3. 11
4. 7

Answer : option (3) 11

Explanation :

prime factors of 225 = `1 × 3 × 3 × 5 × 5

you see, any number which is divisible by 225 only when it has factors of 9 and 25.

• Divisibility rule of 9 : sum of all digits must be divisible by 9.
• Divisibility rule of 25 : last two digits number must be zero or divisible by 25.

we have just given two digits 0 and 1 to form a number which is divisible by 225.

from the divisible rule of 25 , we must choose last two digits zero.

now the sum of number should be 9 so that it can be divided by 9. it is possible only when we take each of 9 digits of the number is 1.

so the number is 11111111100, this is the very number which is divisible by 225. it has 11 digits.

therefore the number of digits in the number is 11. option (3) is correct.

Answer 2

Answer:

Step-by-step explanation: