Understanding the Divisibility Rule for 4
To determine if a number is divisible by 4, we only need to look at the number formed by its last two digits. If the number formed by the last two digits is divisible by 4, then the entire number is divisible by 4.
Applying the Rule to 87893P4
In the given 7-digit number, $87893P4$, the last two digits form the number $P4$. Here, 'P' represents a single digit from 0 to 9.
According to the divisibility rule for 4, the number $87893P4$ will be divisible by 4 if and only if the number $P4$ is divisible by 4.
Finding the Largest Digit for P
We need to find the largest possible digit that can replace P such that the two-digit number $P4$ is divisible by 4. Let's test the possible digits for P, starting from the largest (9) downwards:
- If P = 9: The number formed is 94. Is 94 divisible by 4? $94 \div 4 = 23.5$. No, 94 is not divisible by 4.
- If P = 8: The number formed is 84. Is 84 divisible by 4? $84 \div 4 = 21$. Yes, 84 is divisible by 4.
Since we are looking for the largest number that should replace P, and we found that P=8 works, this is our answer. We don't need to check smaller digits like 2 or 0, although they would also make the number divisible by 4 (forming 24 and 04 respectively).
Conclusion
The largest digit that can replace P in the number $87893P4$ to make it divisible by 4 is 8.
Similar Questions
- Find the smallest non-zero value of k so that 7-digit number 48397k5 is divisible by 9.
- How many of the following numbers are divisible by 3 but not by 9? 2142, 3423, 2430, 4521, 8433, 3258
- If the number 2A19281870B is divisible by both 8 and 11, where A and B are single-digit integers, then the values of A and B are:
- If a number is divisible by both 11 and 13, then it must be:
- If a 9-digit number 937X728Y6 is divisible by 72, then one of the possible values of X + Y is:
- Find the nearest integer to 5347 which is exactly divisible by 137.
- What is the least value of k, so that 23k57 is divisible by 3?
- In a division sum, the divisor is 10 times the quotient and 5 times the remainder. If the remainder is 12, then what is the dividend?
- Which of the following numbers will completely divide $4^{12} + 4^{13} + 4^{14} + 4^{15}$?
- The number 7918378 is divisible by:
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:
