I am a \(3\)-digit number.
The sum of my digits is \(11\).
The product of my digits is \(16\).
My digits are in decreasing order from the hundreds digit to the ones digit.
I have no repeated digits.
What number am I?
We start by determining the ways to multiply three single-digits to get a product of \(16\). Here are the possibilities:
\(1 \times 4 \times 4\) (in any order)
\(1 \times 2 \times 8\) (in any order)
\(2 \times 2 \times 4\) (in any order)
Since the number we are looking for does not have any repeated digits, then the digits in the number must be \(1,\) \(2,\) and \(8\). We can confirm this conclusion by noticing that the sum of these digits is \(1 + 2 + 8 = 11.\)
Since the digits appear in decreasing order, the number must be \(821.\)