Questions: Identify the GCF of the following terms: 34 a^5 b^8 c^3 and 26 a^6 b^2 and 22 a^9 b c^7

Solution Steps

To find the Greatest Common Factor (GCF) of the given terms, we need to:

1. Identify the GCF of the numerical coefficients.
2. Determine the lowest power of each variable that appears in all terms.

The coefficients of the terms are \(34\), \(26\), and \(22\). To find the GCF of these coefficients, we calculate: \[ \text{GCF}(34, 26, 22) = 2 \]

Next, we examine the exponents of the variables \(a\), \(b\), and \(c\) in each term:

• For \(a\): \(5\), \(6\), \(9\)
• For \(b\): \(8\), \(2\), \(1\)
• For \(c\): \(3\), \(0\), \(7\)

We find the minimum exponent for each variable:

• For \(a\): \(\min(5, 6, 9) = 5\)
• For \(b\): \(\min(8, 2, 1) = 1\)
• For \(c\): \(\min(3, 0, 7) = 0\)

Combining the GCF of the coefficients and the minimum exponents, we can express the GCF of the terms as: \[ \text{GCF} = 2a^{5}b^{1}c^{0} \] Since \(c^{0} = 1\), we can simplify this to: \[ \text{GCF} = 2a^{5}b \]

Final Answer