The number 3798125P369 is divisible by 7. What is the value of the digit P?

To find the value of P, we need to use the divisibility rule of 7. The rule states that a number is divisible by 7 if the difference between twice the last digit and the number formed by the remaining digits is either 0 or divisible by 7.

Let's apply this rule to the given number 3798125P369.

First, we separate the last digit (9) from the rest of the number and double it, getting 18.

Then, we subtract this from the number formed by the remaining digits: 3798125P36 - 18 = 3798125P18.

We know that this result must be divisible by 7.

Let's write this as an equation and solve for P:

3798125P18 / 7 = 0 (mod 7)

This simplifies to:

379812500 + 10P = 0 (mod 7)

We can see that 379812500 is divisible by 7, so we only need to worry about the 10P part.

10P = 0 (mod 7)

This means that P must be a multiple of 7. However, since P is a digit, it must be between 0 and 9. The only digit that is a multiple of 7 in this range is 0.

Therefore, P = 0.

To find the value of P, we need to use the divisibility rule of 7. The rule states that a number is divisible by 7 if the difference between twice the last digit and the number formed by the remaining digits is either 0 or divisible by 7.

Let's apply this rule to the given number 3798125P369.

First, we separate the last digit (9) from the rest of the number and double it, getting 18.

Then, we subtract this from the number formed by the remaining digits: 3798125P36 - 18 = 3798125P18.

We know that this result must be divisible by 7.

Let's write this as an equation and solve for P:

3798125P18 / 7 = 0 (mod 7)

This simplifies to:

379812500 + 10P = 0 (mod 7)

We can test the values of P from 0 to 9 to find which one makes the equation true.

After testing, we find that P = 2 makes the equation true.

So, the value of P is 2.