To identify the greatest common factor (GCF) of the numbers \(49\), \(c49c\), and \(2121\), we first need to factor each of the components.
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Factoring \(49\): \[ 49 = 7 \times 7 = 7^2 \]
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Factoring \(2121\): We can find the factors of \(2121\):
- Start with the smallest prime, \(3\): \(2121\) is not divisible by \(3\) (sum of digits is \(6\)).
- Next, check \(5\) (doesn’t end with \(0\) or \(5\)).
- At \(7\): \[ 2121 \div 7 \approx 303, \text{ no exact division (303 > 7)} \] Continuing to \(11\): \[ 2121 \div 11 = 192.8181... \text{(not divisible)} \] Trying \(13\), we perform the division: \[ 2121 \div 13 = 163 \] Check if \(163\) is prime (no smaller prime factors divide \(163\)):
- It is not divisible by \(2\), \(3\), \(5\), \(7\), \(11\). Thus, \(163\) is prime.
Therefore, \[ 2121 = 13 \times 163 \]
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Identifying the GCF: We know:
- \(49 = 7^2\)
- \(2121 = 13 \times 163\)
Now, let’s look at the factors:
- \(49\) has prime factor \(7\).
- \(2121\) has prime factors \(13\) and \(163\).
The GCF is determined by common prime factors. Since \(7\), \(13\), and \(163\) have no factors in common, we conclude: \[ \text{GCF}(49, 2121) = 1 \]
Since the term \(c49c\) isn't a numerical term but seems to contain the number \(49\), we can disregard it for calculation of GCF.
Thus, the greatest common factor of \(49\), \(c49c\), and \(2121\) is: \[ \boxed{1} \]
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