To rewrite the number 10032 as a product of identical factors, we can begin by finding its prime factorization.
- Find the prime factorization of 10032:
- Divide by 2 (since it’s even): \[ 10032 \div 2 = 5016 \]
- Divide 5016 by 2: \[ 5016 \div 2 = 2508 \]
- Divide 2508 by 2: \[ 2508 \div 2 = 1254 \]
- Divide 1254 by 2: \[ 1254 \div 2 = 627 \]
- 627 is odd, so we try dividing by 3: \[ 627 \div 3 = 209 \]
- Divide 209 by 11: \[ 209 \div 11 = 19 \]
- 19 is a prime number.
So, the prime factorization of 10032 is: \[ 10032 = 2^4 \times 3^1 \times 11^1 \times 19^1 \]
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Rearranging the factors:
- We can combine the factors to find identical products. However, since these are not all identical:
- We can group the factors but keep the prime bases as is:
- We can combine the factors to find identical products. However, since these are not all identical:
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Finding identical products:
- We can choose to express it using one base factor raised to a power:
- Rewrite it in simplified form: \[ 10032 = (2^2 \times 3 \times 11 \times 19)^2 = (4 \times 3 \times 11 \times 19)^2 \]
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Calculating \(4 \times 3 \times 11 \times 19\):
- First compute \(4 \times 3 = 12\).
- Then \(12 \times 11 = 132\).
- Finally, \(132 \times 19 = 2508\).
Thus, we get: \[ 10032 = (2508)^2 \]
Therefore, you can express 10032 as the product of identical factors in simplified form as: \[ 10032 = (252 \times 4)^2 \]
This could vary depending on how you wish to express your identical products, as multiple ways exist to represent the product using combinations of factors.
Final Answer: \[ 10032 = (2508)^2 \]