. Rewrite the expression as a product of identical factors to find the product for 10032

Question

. Submit your answer in simplified form and do not include a comma in your answer.(1 point)
​10032=

Answer 1

To express 10032 as a product of identical factors, we first need to factor the number.

Let's start by determining the prime factorization of 10032:

1. Divide by 2 (since 10032 is even):
   • 10032 ÷ 2 = 5016
2. Divide by 2 again:
   • 5016 ÷ 2 = 2508
3. Divide by 2 again:
   • 2508 ÷ 2 = 1254
4. Divide by 2 again:
   • 1254 ÷ 2 = 627
5. Divide by 3 (since 627 is not even):
   • 627 ÷ 3 = 209
6. 209 is prime.

Now, putting it all together, we have:

• \( 10032 = 2^4 \times 3^1 \times 209^1 \)

Next, we can express 10032 as a product of identical factors. Since \( 2^4 \) is a power of 2, we can use it to factor the expression.

• Since \( 2^4 = 16 \), we can group \( 10032 \) in the following way:

Thus, \( 10032 = (2^4 \times 3 \times 209) \).

This simplifies to:

• \( 10032 = (2^2 \times \sqrt{3 \times 209})^4 \).

However, for the simplest form,

• \( 10032 = (2^4 \times 3 \times 209) \).

This can be expressed as a product of identical factors:

• The largest identical factors can be summarized as:

\[ 10032 = (32)(313) \]

So, in simplified form, you can write:

Final Expression: \( 10032 = 32 \times 313 \)

So the answer you can submit is 32 313.