Find the greatest number such that
x172y
is divisible by 45
Why did the number go to therapy?
Because it had too many issues!
Now, let's tackle the problem at hand. To find the greatest number such that x172y is divisible by 45, we need to consider the divisibility rules for 45. A number is divisible by 45 if it is divisible by both 9 and 5.
For a number to be divisible by 9, the sum of its digits must be divisible by 9. In this case, we have x + 1 + 7 + 2 + y = x + 10 + y. In order for this sum to be divisible by 9, x + y should be equal to 8.
Now let's look at the divisibility by 5. The last digit of the number should be either 0 or 5. However, since we're looking for the greatest number, the largest digit for y is 9. So the only option is y = 5.
Based on these conditions, the greatest number satisfying x + y = 8 and y = 5 is x = 3. Therefore, the greatest number is 31725.
Hope that brought a smile to your face while solving the problem! Let me know if there's anything else I can assist you with.
To find the greatest number such that x172y is divisible by 45, we need to consider the divisibility rule of 45.
The divisibility rule of 45 states that a number is divisible by 45 if it is divisible by both 9 and 5.
For a number to be divisible by 9, the sum of its digits must be divisible by 9.
Let's analyze the number x172y:
x + 1 + 7 + 2 + y = x + y + 10
For the number to be divisible by 9, the sum x + y + 10 must be divisible by 9.
Now, let's consider the divisibility rule of 5. A number is divisible by 5 if its last digit is either 0 or 5.
The last digit of x172y is y.
Therefore, for the number to be divisible by 45, we need to find the largest value of y that satisfies both the divisibility rule of 9 and the divisibility rule of 5.
The largest value of y that satisfies the divisibility rule of 9 is 9 (because 9 + 9 + 10 = 28, which is divisible by 9).
For the number to be divisible by 5, y must be either 0 or 5. Since 9 is the largest value for y that satisfies the divisibility rule of 9, the largest value of y that satisfies both the divisibility rule of 9 and the divisibility rule of 5 is 5.
Hence, the greatest number such that x172y is divisible by 45 is x1725.
To find the greatest number such that x172y is divisible by 45, we need to determine the values of x, y, and the conditions for divisibility by 45.
To check if a number is divisible by 45, it must satisfy the following two conditions:
1. The number must be divisible by 5.
2. The sum of its digits must be divisible by 9.
Let's go step by step.
1. The number must be divisible by 5:
To be divisible by 5, the last digit (y) must be either 0 or 5.
2. The sum of its digits must be divisible by 9:
The sum of the digits (1 + 7 + 2 + y) must be divisible by 9.
Now, let's find the possible values of y:
- If y = 0:
The sum of digits will be (1 + 7 + 2 + 0) = 10. Since 10 is not divisible by 9, y = 0 is not a valid solution.
- If y = 5:
The sum of digits will be (1 + 7 + 2 + 5) = 15. Since 15 is divisible by 9, y = 5 is a valid solution.
Therefore, the greatest number such that x172y is divisible by 45 is when y = 5.