To rewrite the expression \(10032\) as a product of identical factors, we first need to factor it completely.
- Start by dividing \(10032\) by \(2\) (the smallest prime number): \[ 10032 \div 2 = 5016 \]
- Divide again by \(2\): \[ 5016 \div 2 = 2508 \]
- Divide again by \(2\): \[ 2508 \div 2 = 1254 \]
- Divide again by \(2\): \[ 1254 \div 2 = 627 \]
- \(627\) is not divisible by \(2\), so we check the next prime number, \(3\): \[ 627 \div 3 = 209 \]
- Now, factor \(209\). It is not divisible by \(2\) or \(3\), but it is divisible by \(11\): \[ 209 \div 11 = 19 \]
- Finally, \(19\) is a prime number.
Putting it all together, the prime factorization of \(10032\) is: \[ 10032 = 2^4 \times 3^1 \times 11^1 \times 19^1 \]
To express it as a product of identical factors, we can find the largest identical factor that can be extracted. The highest power of \(2\) is \(2^4\), which suggests we can take \(2^4\) as a common factor: \[ 10032 = (2^4) \times (3 \times 11 \times 19) \] Now calculate \(3 \times 11 \times 19\): \[ 3 \times 11 = 33, \] \[ 33 \times 19 = 627. \] Thus, \[ 10032 = 16 \times 627. \]
We can also express \(10032\) in terms of identical factors: \[ 10032 = (2^4) \times (3 \times 11 \times 19) = (2^4) \times 627. \] To express this in a simpler way, we can observe that \(10032\) can be represented as: \[ 10032 = (2^4 \times 3 \times 11 \times 19). \]
Now to fit into your format of submitting it in simplified form without a comma:
\[ 10032= 2^4 \times 3 \times 11 \times 19 \]
If you want a product of identical factors: \[ 10032 = 16 \times 627 \]
After analyzing, if the goal is to find a product of identical factors, that would involve repeating factors; however, the simplest form can be shown as: \[ 10032 = 2^4 \times 627 \]
So a simplified answer can simply be:
10032=2^4 * 627
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