Find the least number by which 8232 must be divided  to obtain a perfect cube write the cube root of the number so obtained 

To solve this problem, we need to find the smallest number by which 8232 must be divided to obtain a perfect cube, and then find the cube root of the resulting number.

### Step 1: Prime Factorization of 8232
We begin by performing the prime factorization of 8232:

\[
8232 \div 2 = 4116
\]
\[
4116 \div 2 = 2058
\]
\[
2058 \div 2 = 1029
\]
\[
1029 \div 3 = 343
\]
\[
343 = 7^3
\]

Thus, the prime factorization of 8232 is:
\[
8232 = 2^3 \times 3 \times 7^3
\]

### Step 2: Identify Missing Factors to Make a Perfect Cube
For a number to be a perfect cube, the exponents of all its prime factors must be multiples of 3. In the prime factorization of 8232, we see:

- \(2^3\) is already a cube.
- \(3^1\) is not a cube (it needs two more factors of 3).
- \(7^3\) is already a cube.

So, we need to divide by \(3\) (to remove the extra factor of 3) to make it a perfect cube.

### Step 3: Divide 8232 by 3
\[
\frac{8232}{3} = 2744
\]

### Step 4: Find the Cube Root of 2744
Now, we find the cube root of 2744:
\[
\sqrt[3]{2744} = 14
\]

### Conclusion:
- The least number by which 8232 must be divided to obtain a perfect cube is **3**.
- The cube root of the resulting number (2744) is **14**.

Would you like further clarification or additional details?

Here are 5 related questions to deepen your understanding:
1. How is the prime factorization method useful in determining perfect cubes?
2. What happens if a number's prime factors all have exponents that are multiples of 3?
3. How would you find the least number to multiply by, instead of divide, to get a perfect cube?
4. What other methods can be used to check if a number is a perfect cube?
5. How can you apply this method to much larger numbers?

**Tip:** When checking for perfect cubes, always ensure that the exponents in the prime factorization are divisible by 3.

Find the least number by which 8232 must be divided to obtain a perfect cube. Write the cube root of the number so obtained.

Discover how to find the least number by which 8232 must be divided to obtain a perfect cube. This solution explains prime factorization, perfect cubes, and cube roots, suitable for students in Grades 6-8.

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