Question

Identify the greatest common factor of 36, z36z and 1212.

Answer 1

To identify the greatest common factor (GCF) of the numbers 36, z36z, and 1212, we first need to clarify the terms.

1. **Understanding Each Term**:
- 36: This is a clear integer.
- z36z: It seems to be a variable expression, but without further context, we will treat it as an integer if it can be interpreted or if the variable \( z \) takes on certain integer values.
- 1212: This is also a clear integer.

2. **Finding GCF of the Known Integers**:
- First, we determine the prime factorization of the integers.

- **For 36**:
\[
36 = 6 \times 6 = 2^2 \times 3^2
\]

- **For 1212**:
\[
1212 = 121 \times 10 = (11^2 \times 2 \times 5) \text{ or factorizing further }:
\]

Dividing by 2:
\[
1212 \div 2 = 606
\]
Dividing by 2 again:
\[
606 \div 2 = 303
\]
Dividing 303 by 3:
\[
303 \div 3 = 101
\]
Thus,
\[
1212 = 2^2 \times 3^1 \times 101
\]

3. **Finding the GCF**:
- To find the GCF, we take the lowest power of each prime factor present in both numbers:
- For \(2\): Minimum of 2 in 36 and 1 in 1212 is 2.
- For \(3\): Minimum of 2 in 36 and 1 in 1212 is 1.

Thus,
\[
\text{GCF}(36, 1212) = 2^2 \times 3^1 = 4 \times 3 = 12.
\]

4. **Considering z36z**:
- The factorization is dependent on \(z\). If \(z\) represents an integer, we can evaluate \(z36z\) accordingly. If \(z = 1\), \(z = 2\), etc., the GCF may change based on the actual value chosen.

In summary, without an explicit value for \(z\), the final GCF considering only the known integers (36 and 1212) is:

\[
\text{GCF} = 12.
\]

For evaluating \(GCF\) with \(z36z\), more context or specification regarding \(z\) would be necessary.