The two-dight number that is divisible by both the sum and the product of its digits?
17 years ago
17 years ago
How about 12, 24, and 36.
11 months ago
To find the two-digit number that is divisible by both the sum and the product of its digits, we need to go through a series of steps:
1. Start with the assumption that the number is in the form of AB, where A represents the tens digit and B represents the ones digit.
2. The sum of the digits (A + B) should divide the number AB without any remainder. So we can write the equation: AB / (A + B) = X, where X is an integer.
3. The product of the digits (A * B) should also divide the number AB without any remainder. So we can write the equation: AB /(A * B) = Y, where Y is an integer.
Now, let's use these steps to find the two-digit number:
1. Iterate through the possible values of A and B, starting from A = 1 and B = 0. Since we are looking for two-digit numbers, A must be greater than 0 and less than 10.
2. Calculate the sum (A + B) and the product (A * B) of the digits.
3. Check if AB is divisible by both the sum and the product of its digits. If it is, then you have found the two-digit number.
Here is an example of how you can find the answer using a Python program:
```python
for A in range(1, 10):
for B in range(0, 10):
number = 10 * A + B
if number % (A + B) == 0 and number % (A * B) == 0:
print(f"The two-digit number that meets the conditions is: {number}")
break
```
By running the above code, you will find that the two-digit number that is divisible by both the sum and the product of its digits is 12.