QQuestionMathematics
QuestionMathematics
Find the greatest perfect square that is a factor of 52.
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Step 1:I'll solve this problem step by step, following the specified LaTeX formatting guidelines:
Step 2:: Understand the Problem
We need to find the largest perfect square that divides 52 evenly. A perfect square is a number that can be expressed as the product of an integer with itself.
Step 3:: Prime Factorization
52 = 2^{2} \times 13
Let's first find the prime factorization of 52:
Step 4:: Identify Perfect Square Factors
- $$13^{1}$$ is not a perfect square
To be a perfect square, the exponents of prime factors must be even numbers.
Step 5:: Calculate the Largest Perfect Square Factor
The largest perfect square factor is $$2^{2} = 4
Step 6:: Verify the Result
- $$52 \div 4 = 13$$ (which is an integer)
- 4 is the largest perfect square that divides 52 evenly
Final Answer
4 is the greatest perfect square factor of 52.
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