ИИ:
Let's solve this step by step:
We need a three-digit number whose digits multiply to 219 and add up to 19. Let the three digits be
𝑎
,
𝑏
,
and
𝑐
. The following conditions must be true:
𝑎
⋅
𝑏
⋅
𝑐
=
219
𝑎
+
𝑏
+
𝑐
=
19
We also want to find the greatest three-digit number, so we'll prioritize larger values for the hundreds place digit (
𝑎
).
Factoring 219
The prime factorization of 219 is:
219
=
3
⋅
73
Thus, the digits must multiply to 219. By trial and error, let's explore combinations of three digits that satisfy these constraints:
Possible Combinations
Start by finding factors of 219 that are digits (1 to 9), keeping their sum equal to 19:
The factors
3
,
9
,
and
7
work because:
3
⋅
9
⋅
7
=
219
and
3
+
9
+
7
=
19.
Building the Largest Number
To form the largest three-digit number, arrange the digits
3
,
9
,
and
7
in descending order:
973.
Thus, the greatest three-digit number Cathy’s address can contain is 973.
