Which is NOT a factor pair for 60? A) (2, 30) B) (3, 20) C) (4, 12) D) (6, 10)
Which is NOT a factor pair for 60? A) (2, 30) B) (3, 20) C) (4, 12) D) (6, 10)
The Correct Answer and Explanation is:
Correct Answer: C) (4, 12)
To identify the incorrect factor pair of 60, begin by understanding the concept of factor pairs. A factor pair consists of two whole numbers that multiply to give a specific product. For the number 60, every valid factor pair should satisfy the equation:
First Number × Second Number = 60
Now, evaluate each option:
- Option A (2, 30):
2 × 30 = 60 → This is a valid factor pair. - Option B (3, 20):
3 × 20 = 60 → This is a valid factor pair. - Option C (4, 12):
4 × 12 = 48 → This does not equal 60. Hence, this pair is not a valid factor pair. - Option D (6, 10):
6 × 10 = 60 → This is a valid factor pair.
The multiplication in Option C does not result in 60, indicating that (4, 12) is not a true factor pair for the number 60. This conclusion is based purely on arithmetic verification, without assuming any abstract properties.
Understanding factor pairs helps in multiple mathematical areas, including simplifying fractions, solving equations, and analyzing numerical relationships. For a positive integer like 60, identifying all valid factor pairs involves finding all whole numbers that divide it evenly. These pairs usually include smaller numbers with their corresponding larger counterparts. The list of actual factor pairs of 60 includes:
(1, 60), (2, 30), (3, 20), (4, 15), (5, 12), (6, 10)
The pair (4, 12), although made of two factors of 60 individually, does not multiply to the target product, making it invalid as a pair. Hence, Option C stands out as the correct response to this question.
