Math Problem Statement
Solution
The problem asks you to find a number that meets the following criteria:
- It is a factor of 36.
- It is a multiple of 3.
- The sum of its two digits is a square number.
- The product of its two digits is a cube.
Let's break it down:
Step 1: Find factors of 36
The factors of 36 are: 1, 2, 3, 4, 6, 9, 12, 18, and 36.
Step 2: Find multiples of 3
Since the number must be a multiple of 3, it needs to be divisible by 3. From the factors of 36, the multiples of 3 are: 3, 6, 9, 12, 18.
Step 3: Check if the sum of its two digits is a square number
We now look at the two-digit multiples of 3 from the previous step. The candidates are 12, 18.
- For 12, the sum of the digits is , which is not a square number.
- For 18, the sum of the digits is , which is a square number ().
Step 4: Check if the product of its two digits is a cube
For 18, the product of the digits is , which is a cube number ().
Conclusion:
The number that satisfies all four criteria is 18.
Would you like further explanations or help with similar problems? Here are some related questions for practice:
- What are the factors of 36 and how do you list them?
- How do you determine if a number is a multiple of 3?
- How can you check if the sum of two digits forms a square number?
- How do you verify if the product of two digits is a cube?
- What other numbers could be factors of 36 and meet certain mathematical criteria?
Tip: When solving problems that involve multiple conditions, it’s often useful to break the problem down step by step, testing each condition individually.
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Math Problem Analysis
Mathematical Concepts
Factors
Multiples
Square Numbers
Cube Numbers
Formulas
Sum of digits
Product of digits
Theorems
Factors of a number
Multiples of a number
Properties of square numbers
Properties of cube numbers
Suitable Grade Level
Grades 6-8
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