Question

Identify the greatest common factor of 49, c49c and 2121.

Answer 1

To identify the greatest common factor (GCF) of the numbers \(49\), \(c49c\), and \(2121\), we first need to factor each of the components.

1. **Factoring \(49\)**:
\[
49 = 7 \times 7 = 7^2
\]

2. **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,
\[
2121 = 13 \times 163
\]

3. **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:
\[
\boxed{1}
\]