To find the three-digit number on the license plate that meets the given conditions, let's denote the digits as \( a \), \( b \), and \( c \) where \( a \geq b \geq c \). The conditions we need to satisfy are:
- \( a \cdot b \cdot c = 210 \)
- \( a + b + c = 18 \)
Let's start by finding the factors of 210 to identify suitable digits.
The prime factorization of 210 is: \[ 210 = 2 \times 3 \times 5 \times 7 \]
Now, we need to combine these factors into three digits (each between 0 and 9) such that their product is 210 and their sum is 18.
Let's try different combinations of digits such that their products yield 210:
- Looking at the individual factors: If we try \( 7 \), \( 5 \), and \( 6 \):
- \( 7 \cdot 5 \cdot 6 = 210 \)
- \( 7 + 5 + 6 = 18 \)
Both conditions are satisfied. Now, since the numbers must be in descending order:
Thus, the digits are \( 7, 6, 5 \), and the license plate number is 765.
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