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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.