To find the greatest common factor (GCF) of the numbers 7, \( y^7 \), and 4949, we first need to analyze each of these terms.
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Identify the factors of each term:
- 7: The factors of 7 are 1 and 7.
- \( y^7 \): The only factors here are powers of \( y \), which are \( y^0 \) (1), \( y^1 \), ..., up to \( y^7 \).
- 4949: We need to factor 4949 to identify its prime factors.
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Factor 4949:
- We can divide 4949 by 7 as follows: \[ 4949 \div 7 = 707 \]
- Next, we can factor 707 further: \[ 707 = 7 \times 101 \]
- Therefore, \( 4949 = 7^2 \times 101 \).
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Now identify the GCF:
- The factors of each term:
- For 7: The factors are 1 and 7.
- For \( y^7 \): The factors are \( y^0 = 1 \), \( y^1 \), ..., \( y^7 \).
- For 4949: The prime factor is \( 7^2 \times 101 \).
- The factors of each term:
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Compare all terms:
- The common factor from the numbers 7 and 4949 is 7.
- The term \( y^7 \) does not have any numerical factors since it contains the variable \( y \).
The common factors among all three terms are limited since \( y^7 \) introduces a variable that does not contribute to numerical factors.
Thus, the GCF of 7, \( y^7 \), and 4949 is simply:
\[ \boxed{7} \]