Which of the following expression(s)are true?
I. 337 is a prime number.
II. The number 12 has 6 positive factors.
III. 3272418 completely divisible by 9.

Options

A. Only I
B. Only I and II
C. Only II and III
D. All expressions are true

Answer

To determine which of the given expressions are true, we will evaluate each statement one by one.

### Step 1: Evaluate Expression I
**Expression I:** 337 is a prime number.

- A prime number is defined as a number greater than 1 that has no positive divisors other than 1 and itself.
- The only factors of 337 are 1 and 337.
- Therefore, 337 is a prime number.

**Conclusion for Expression I:** True

### Step 2: Evaluate Expression II
**Expression II:** The number 12 has 6 positive factors.

- To find the positive factors of 12, we can list them:
- The factors of 12 are: 1, 2, 3, 4, 6, and 12.
- Counting these, we find that there are indeed 6 positive factors.

**Conclusion for Expression II:** True

### Step 3: Evaluate Expression III
**Expression III:** 3272418 is completely divisible by 9.

- A number is divisible by 9 if the sum of its digits is divisible by 9.
- Let's calculate the sum of the digits of 3272418:
- 3 + 2 + 7 + 2 + 4 + 1 + 8 = 27
- Now, we check if 27 is divisible by 9:
- 27 ÷ 9 = 3, which is an integer.
- Therefore, 3272418 is divisible by 9.

**Conclusion for Expression III:** True

### Final Conclusion
All three expressions are true:
- Expression I: True
- Expression II: True
- Expression III: True

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