Divisibility Rule for 3: Finding k
To determine the value of k that makes the number 345k6 divisible by 3, we use the divisibility rule for 3.
Divisibility Rule Explanation
A number is divisible by 3 if the sum of its individual digits is divisible by 3.
Applying the Rule to 345k6
First, sum the known digits of the number 345k6:
\(3 + 4 + 5 + 6 = 18\)
The total sum of the digits is \(18 + k\).
Condition for Divisibility
For 345k6 to be divisible by 3, the sum \(18 + k\) must be a multiple of 3.
Since 18 is already divisible by 3 (\(18 = 3 \times 6\)), for \(18 + k\) to be divisible by 3, k must also be a digit (0 through 9) that is divisible by 3.
Testing the Options
Let's check the given options for k:
- Option 1 (k=1): Sum = \(18 + 1 = 19\). 19 is not divisible by 3.
- Option 2 (k=4): Sum = \(18 + 4 = 22\). 22 is not divisible by 3.
- Option 3 (k=6): Sum = \(18 + 6 = 24\). 24 is divisible by 3 (\(24 \div 3 = 8\)).
- Option 4 (k=2): Sum = \(18 + 2 = 20\). 20 is not divisible by 3.
Conclusion
The value k = 6 satisfies the condition, making the number 345k6 divisible by 3.
Similar Questions
- Find the four-digit dividend of 21, 42, 147 and 105 that will give the remainder 14, 35, 140 and 98, respectively.
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- If x is the greatest 4-digit number that is divisible by 237, then the sum of digits of x is:
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Important Questions from Divisibility and Remainder
If the 8-digit number 888x53y4 is divisible by 72, then what is the value of (7x + 2y), for the maximum value of y?
If all positive divisors of 132 are arranged in descending order, then what digit will be at unit place of first divisor ?
If 3 2019 is divided by 10, then what is the remainder?
The number 3798125P369 is divisible by 7. What is the value of the digit P?
Consider all 3-digit numbers (without repetition of digits) obtained using three non-zero digits which are multiples of 3. Let S be their sum.
Which of the following is/are correct?
1. S is always divisible by 74.
2. S is always divisible by 9.
select the correct answer using the code given below:
