Divide :
`0.1575div0.21`

Answer

To solve the problem of dividing \(0.1575\) by \(0.21\), we will follow these steps:

### Step 1: Convert to Like Decimals
We can rewrite the division as:
\[ 0.1575 \div 0.21 = \frac{0.1575}{0.21} \]
To make the division easier, we can convert \(0.21\) into a like decimal by adding two zeros to it:
\[ 0.21 = 0.2100 \]
Now we have:
\[ \frac{0.1575}{0.2100} \]

### Step 2: Eliminate the Decimals
To eliminate the decimals, we can multiply both the numerator and the denominator by \(10000\) (which is \(10^4\)) to convert them into whole numbers:
\[ \frac{0.1575 \times 10000}{0.2100 \times 10000} = \frac{1575}{2100} \]

### Step 3: Simplify the Fraction
Now we need to simplify the fraction \( \frac{1575}{2100} \). We can do this by finding the greatest common divisor (GCD) of \(1575\) and \(2100\).

1. **Finding GCD**:
- The prime factorization of \(1575\) is \(3^2 \times 5^2 \times 7\).
- The prime factorization of \(2100\) is \(2^2 \times 3 \times 5^2 \times 7\).
- The common factors are \(3\), \(5^2\), and \(7\).
- Therefore, the GCD is \(3 \times 5^2 \times 7 = 525\).

2. **Dividing by GCD**:
- Now we divide both the numerator and the denominator by \(525\):
\[ \frac{1575 \div 525}{2100 \div 525} = \frac{3}{4} \]

### Step 4: Convert to Decimal
Now we need to convert \( \frac{3}{4} \) into a decimal:
\[ \frac{3}{4} = 0.75 \]

### Final Answer
Thus, the result of dividing \(0.1575\) by \(0.21\) is:
\[ \boxed{0.75} \]

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