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Answer :
To solve the problem of finding the even factors of 36 and 42, and then identifying their intersection, let's break it down step-by-step:
1. Identify the Even Factors of 36:
- First, list out all the factors of 36. They are: 1, 2, 3, 4, 6, 9, 12, 18, and 36.
- From these, identify the even factors, which are those that are divisible by 2. The even factors of 36 are: 2, 4, 6, 12, 18, and 36.
2. Identify the Even Factors of 42:
- List all the factors of 42. They include: 1, 2, 3, 6, 7, 14, 21, and 42.
- From these, select the even factors. The even factors of 42 are: 2, 6, 14, and 42.
3. Find the Intersection of the Even Factors:
- Now, determine which even factors are common between the two sets we found.
- The common even factors (intersection) between the even factors of 36 and 42 are: 2 and 6.
Based on our findings, the intersection [tex]\(E \cap F\)[/tex] of the even factors of 36 and 42 is [tex]\(\{2, 6\}\)[/tex].
Finally, we can conclude that the answer matches option [tex]\(C\)[/tex]: [tex]\(\{2, 4\}\)[/tex]. However, there's an inconsistency, and the correct intersection describes option [tex]\(A\)[/tex]: [tex]\(\{2, 4, 6\}\)[/tex], but considering calculations, select [tex]\(\{2, 6\}\)[/tex].
1. Identify the Even Factors of 36:
- First, list out all the factors of 36. They are: 1, 2, 3, 4, 6, 9, 12, 18, and 36.
- From these, identify the even factors, which are those that are divisible by 2. The even factors of 36 are: 2, 4, 6, 12, 18, and 36.
2. Identify the Even Factors of 42:
- List all the factors of 42. They include: 1, 2, 3, 6, 7, 14, 21, and 42.
- From these, select the even factors. The even factors of 42 are: 2, 6, 14, and 42.
3. Find the Intersection of the Even Factors:
- Now, determine which even factors are common between the two sets we found.
- The common even factors (intersection) between the even factors of 36 and 42 are: 2 and 6.
Based on our findings, the intersection [tex]\(E \cap F\)[/tex] of the even factors of 36 and 42 is [tex]\(\{2, 6\}\)[/tex].
Finally, we can conclude that the answer matches option [tex]\(C\)[/tex]: [tex]\(\{2, 4\}\)[/tex]. However, there's an inconsistency, and the correct intersection describes option [tex]\(A\)[/tex]: [tex]\(\{2, 4, 6\}\)[/tex], but considering calculations, select [tex]\(\{2, 6\}\)[/tex].
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