To find the greatest common factor (GCF) of the terms in the expression \(30m + 12n\), we look for the GCF of the coefficients and also consider the variables.
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Find the GCF of the coefficients:
- The coefficients are 30 and 12.
- The prime factorization of 30 is \(2 \times 3 \times 5\).
- The prime factorization of 12 is \(2^2 \times 3\).
The common prime factors are \(2\) and \(3\). The least power of these common factors gives us:
- For \(2\), the minimum power is \(2^1\).
- For \(3\), the minimum power is \(3^1\).
Thus, the GCF of 30 and 12 is: \[ 2^1 \times 3^1 = 2 \times 3 = 6. \]
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Consider the variables:
- The term \(30m\) has the variable \(m\) and \(12n\) has the variable \(n\).
- Since there are no common variable factors, their GCF is \(1\).
Combining both parts, the GCF of \(30m + 12n\) is simply the GCF of the coefficients: \[ \text{GCF} = 6. \]
Thus, the GCF of the expression \(30m + 12n\) is 6.
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