Examine if 1512 is a perfect cube .If not find the smallest number by which it must be multiplied so that the product is a perfect cube .Also find the smallest number by which it must be divided so that the quotient is a perfect cube.

Explanation

To determine if 1512 is a perfect cube, we will first perform its prime factorization. Then, we will analyze the factors to see if any adjustments are needed to make it a perfect cube.

### Step 1: Prime Factorization of 1512
We will divide 1512 by the smallest prime numbers until we reach 1.

1. Divide by 2:
- \( 1512 \div 2 = 756 \)
- \( 756 \div 2 = 378 \)
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