A smallest possible number which is divisible by either 3,5 or 7 when represented by only two digits either 0 or 1, then the minimum number of digits required to represent it :

Options

A. 6
B. 5
C. 7
D. can't be determined

Answer

To solve the problem of finding the smallest possible number that is divisible by either 3, 5, or 7 and can be represented using only two digits (0 or 1), we will follow these steps:

### Step 1: Identify the range of two-digit numbers
The two-digit numbers range from 10 to 99.

### Step 2: List the smallest two-digit numbers divisible by 3, 5, or 7
We will check each two-digit number starting from 10 to find the smallest number divisible by 3, 5, or 7.

- **Divisibility by 3**: A number is divisible by 3 if the sum of its digits is divisible by 3.
- **Divisibility by 5**: A number is divisible by 5 if it ends in 0 or 5.
- **Divisibility by 7**: A number is divisible by 7 if the number can be divided by 7 without a remainder.

### Step 3: Check each number
We will start checking from 10:

- 10: Not divisible by 3, 5, or 7
- 11: Not divisible by 3, 5, or 7
- 12: Divisible by 3 (12 ÷ 3 = 4)
- 13: Not divisible by 3, 5, or 7
- 14: Divisible by 7 (14 ÷ 7 = 2)
- 15: Divisible by 5 (15 ÷ 5 = 3)
- 16: Not divisible by 3, 5, or 7
- 17: Not divisible by 3, 5, or 7
- 18: Divisible by 3 (18 ÷ 3 = 6)
- 19: Not divisible by 3, 5, or 7
- 20: Divisible by 5 (20 ÷ 5 = 4)
- 21: Divisible by 3 (21 ÷ 3 = 7)
- 22: Not divisible by 3, 5, or 7
- 23: Not divisible by 3, 5, or 7
- 24: Divisible by 3 (24 ÷ 3 = 8)
- 25: Divisible by 5 (25 ÷ 5 = 5)
- 26: Not divisible by 3, 5, or 7
- 27: Divisible by 3 (27 ÷ 3 = 9)
- 28: Divisible by 7 (28 ÷ 7 = 4)
- 29: Not divisible by 3, 5, or 7
- 30: Divisible by 3 (30 ÷ 3 = 10), also divisible by 5 (30 ÷ 5 = 6)

The smallest two-digit number that is divisible by either 3, 5, or 7 is **12**.

### Step 4: Convert the number to binary
Now we need to convert the smallest number (12) to binary.

- 12 in binary:
- 12 divided by 2 = 6, remainder 0
- 6 divided by 2 = 3, remainder 0
- 3 divided by 2 = 1, remainder 1
- 1 divided by 2 = 0, remainder 1

Reading the remainders from bottom to top, we get:
- 12 in binary is **1100**.

### Step 5: Count the number of digits in binary
The binary representation of 12 (which is 1100) has **4 digits**.

### Final Answer
The minimum number of digits required to represent the smallest possible number (12) in binary is **4**.

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