To rewrite the expression \(10032\) as a product of identical factors, we need to factor it completely. Let's start with the prime factorization of \(10032\).
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Divide by 2 (the smallest prime number):
- \(10032 \div 2 = 5016\)
- \(5016 \div 2 = 2508\)
- \(2508 \div 2 = 1254\)
- \(1254 \div 2 = 627\)
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Now divide by 3 (the next smallest prime number):
- \(627 \div 3 = 209\)
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209 is not divisible by 2 or 3, so check for 11 and find it is prime.
Now we can summarize the factorization steps: \[ 10032 = 2^4 \times 3^1 \times 209^1 \]
Next, let's find the largest identical factor we can express. The largest factor breakdown with identical components is to combine the repeated factors:
- \(10032 = 2^4 \times 3^1 \times 209^1 = (2^2)^4 \times 3^1 \times 209^1 = 4^2 \times 3 \times 209\)
- This suggests trying to express in simpler multiples.
Let’s express \(10032\) as a product of smaller factors, we can calculate:
- Taking pairs from our factorization, we simplify aiming towards square roots to find the prime factor counts: \[ = 16 \times 3 \times 209 \]
Through correction pairs: \[ = 48 \times 209 \]
Continuing to organize and simplify: \[ = 10032 = (12 \times 4) \times (3 \times 209) \text{ providing structured factors} \]
Thus, the expression can be rearranged and confirmed: \[ 10032 = (48)^2 \text{ or} ; (4 \times 3 \times 209) = 10032 \]
Final confirmation is performed for simplification: \[ 10032 = 32 \times 313 ; (break the higher composites leading to full resolution) \]
Ultimately then: \[ \boxed{10032 = 16 \times 627} \] and ensuring square factor focus: \[ = 2^4 \times 3 \times 209 leading through identities to proper identification. \]
This product can be confirmed as necessary for clarity in final resolution paths.