The smallest number with which 16 should be multipled to make it a perfect cube is __________

Answer

To find the smallest number with which 16 should be multiplied to make it a perfect cube, we can follow these steps:

### Step-by-Step Solution:

1. **Prime Factorization of 16**:
- First, we need to express 16 as a product of its prime factors.
- 16 can be written as \( 2 \times 2 \times 2 \times 2 \) or \( 2^4 \).

2. **Understanding Perfect Cubes**:
- A perfect cube is a number that can be expressed as \( a^3 \), where \( a \) is an integer.
- For a number to be a perfect cube, all the prime factors in its factorization must have exponents that are multiples of 3.

3. **Analyzing the Exponent of 2**:
- In the factorization \( 2^4 \), the exponent of 2 is 4.
- To make this a perfect cube, we need the exponent to be a multiple of 3. The closest multiple of 3 that is greater than or equal to 4 is 6.

4. **Calculating the Required Multiplication**:
- To increase the exponent from 4 to 6, we need to add 2 more factors of 2 (since \( 2^6 = 2^4 \times 2^2 \)).
- Therefore, we need to multiply 16 by \( 2^2 \) (which is 4).

5. **Final Answer**:
- The smallest number with which 16 should be multiplied to make it a perfect cube is **4**.

### Summary:
Thus, the answer is **4**.

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