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Step 1:I'll solve this step-by-step using the specified LaTeX formatting guidelines:
Step 2:: Understand the Problem
To find all factor pairs of 42, we need to identify all pairs of positive integers that, when multiplied together, equal 42.
Step 3:: List the Factors of 42
1, 2, 3, 6, 7, 14, 21, 42
First, let's find all the factors of 42:
Step 4:: Create Factor Pairs
Now, we'll pair these factors to create all possible factor pairs:
Step 5:1 \times 42 = 42
2. $$2 \times 21 = 42
Step 6:3 \times 14 = 42
4. $$6 \times 7 = 42
Step 7:: List the Factor Pairs
The factor pairs of 42 are:
Step 8:(1, 42)
2. $$(2, 21)
Step 9:(3, 14)
4. $$(6, 7)
Final Answer
The factor pairs of 42 are: (1, 42), (2, 21), (3, 14), and (6, 7).
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