To identify the greatest common factor (GCF) of the numbers 36, z36z, and 1212, we first need to clarify the terms.
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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.
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Finding GCF of the Known Integers:
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First, we determine the prime factorization of the integers.
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For 36: \[ 36 = 6 \times 6 = 2^2 \times 3^2 \]
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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, \[ 1212 = 2^2 \times 3^1 \times 101 \]
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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, \[ \text{GCF}(36, 1212) = 2^2 \times 3^1 = 4 \times 3 = 12. \]
- To find the GCF, we take the lowest power of each prime factor present in both numbers:
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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.
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