Question

Question
Rewrite the expression as a product of identical factors to find the product for 10032
. Submit your answer in simplified form.



(1 point)

Answer 1

To rewrite the expression for \( 10032 \) as a product of identical factors, we first need to factor the number.

Let's find the prime factorization of \( 10032 \).

1. **Divide by 2:**
\[
10032 \div 2 = 5016
\]
2. **Divide by 2 again:**
\[
5016 \div 2 = 2508
\]
3. **Divide by 2 again:**
\[
2508 \div 2 = 1254
\]
4. **Divide by 2 again:**
\[
1254 \div 2 = 627
\]
5. **Divide by 3 (next prime):**
\[
627 \div 3 = 209
\]
6. **Divide 209 by its prime factors (it is \( 11 \times 19 \)):**
- \( 209 = 11 \times 19 \)

Now, compiling all the factors:
\[
10032 = 2^4 \times 3^1 \times 11^1 \times 19^1
\]

Identifying the number of identical factors:
- The \( 2^4 \) means you can express this as \( (2^2 \times 2^2) \) or \( (4 \times 4) \).

Now, let's rewrite \( 10032 \) in a simplified form:
\[
10032 = 16 \times 627
\]

To express \( 10032 \) as a product of identical factors, we can take the 16 (which is \( 2^4 \)).
Thus, the product can be expressed as:
\[
10032 = 16 \times 3 \times 11 \times 19
\]

But the most straightforward representation for identical factors would be as:
\[
10032 = (4^2) \cdot (3 \cdot 11 \cdot 19)
\]

Final answer discussing identical factors:
We can simply state:
\[
10032 = (16) \cdot (627) \text{ thus can say } = (4 \cdot 4) \cdot (3 \cdot 11 \cdot 19)
\]

Hence, the expression for \( 10032 \) as a product of identical factors can be \( (16) \) of \( 627 \).

In the format requested, the simplest form is:
\[
\boxed{10032 = 16 \cdot 627}
\]