Write the converse of the following statement: 'A positive integer is prime only if it has no divisors other that 1 and itself.'

Answer

To find the converse of the statement "A positive integer is prime only if it has no divisors other than 1 and itself," we can follow these steps:

### Step 1: Identify the components of the original statement
The original statement can be broken down into two parts:
- **P**: A positive integer is prime.
- **Q**: It has no divisors other than 1 and itself.

The original statement can be expressed in the form "P only if Q," which means that if P is true, then Q must also be true.

### Step 2: Write the converse
The converse of a statement of the form "P only if Q" is "Q only if P." This means we need to reverse the roles of P and Q.

### Step 3: Formulate the converse
Thus, the converse of the statement is:
"A positive integer has no divisors other than 1 and itself only if it is a prime."

### Final Statement
The final converse statement is:
"A positive integer has no divisors other than 1 and itself only if it is a prime."

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