- Identify all divisors of \(28\) by testing integers up to \(\sqrt{28} \approx 5.29\): \(1, 2, 4, 7, 14, 28\).
- Determine the factor pairs by dividing \(28\) by each divisor: \((1, 28)\), \((2, 14)\), and \((4, 7)\).
- Select an alternative to the given pair \((4, 7)\) from the list.
- Conclude that \(\boxed{2}\) and \(\boxed{14}\) are a factor pair of \(28\).
Explanation
- Problem Analysis and Definition of Factor Pairs
To find factor pairs of the number \(28\), we look for pairs of positive integers that, when multiplied together, yield a product of \(28\). A factor pair \((a, b)\) satisfies the equation \(a \times b = 28\). The divisors of \(28\) are integers that divide \(28\) without leaving a remainder. We can identify these divisors by testing integers from \(1\) up to \(\sqrt{28} \approx 5.29\).
- Identifying Factors of 28
Checking integers from \(1\) to \(5\):
- For \(1\): \(28 \div 1 = 28\), so \((1, 28)\) is a factor pair.
- For \(2\): \(28 \div 2 = 14\), so \((2, 14)\) is a factor pair.
- For \(3\): \(28 \div 3 = 9.33\dots\), so \(3\) is not a divisor.
- For \(4\): \(28 \div 4 = 7\), so \((4, 7)\) is a factor pair.
- For \(5\): \(28 \div 5 = 5.6\), so \(5\) is not a divisor.
The distinct factor pairs are \((1, 28)\), \((2, 14)\), and \((4, 7)\).
- Final Answer Selection
The problem asks for a factor pair of \(28\) other than \((4, 7)\). Based on our list, we have two other options: \((1, 28)\) and \((2, 14)\). We can choose either one to complete the sentence. Let's select \(2\) and \(14\). Thus, \(2\) and \(14\) are a factor pair of \(28\) because \(2 \times 14 = 28\).
Examples
Factor pairs are essential in real-life situations involving grouping items equally. For instance, if you have 28 students in a class and need to arrange them in equal rows for a photo, finding factor pairs helps you determine the possible configurations. You could arrange them in 2 rows of 14 students, 4 rows of 7 students, or even 1 row of 28 students. Identifying these pairs allows for flexible and efficient organization in various daily tasks, from event planning to arranging furniture in a room.