Question

Jim list three factor pairs of 54 as
1 x 54 or 2 x 27 or 6 x 9.
Which factor pair has a prime number?
Explain why the factors are prime or not

Answer 1

Let's analyze the factor pairs of 54 that Jim listed:

1. **1 x 54**
- 1 is not considered a prime number.
- 54 is not a prime number because it has factors other than 1 and itself (such as 2 x 27, for example).

2. **2 x 27**
- 2 is a prime number because its only positive divisors are 1 and 2.
- 27 is not a prime number as it can be factored into 3 x 9 (and further into 3 x 3 x 3).

3. **6 x 9**
- 6 is not a prime number since it can be factored into 2 x 3.
- 9 is not a prime number as it can be factored into 3 x 3.

Among the factor pairs listed, **the factor pair 2 x 27 contains a prime number (2)**.

In summary:
- Prime numbers are numbers greater than 1 that have no positive divisors other than 1 and themselves.
- In the pairs listed, only **2** meets this definition of being a prime number.