Question

find the greatest common factor of the expressions.
24a¹²b³, 12a⁴, 36a³b⁵

Explanation:

Step1: Find GCF of coefficients

Find GCF of 24, 12, 36. Factors of 24: 1,2,3,4,6,8,12,24; 12:1,2,3,4,6,12; 36:1,2,3,4,6,9,12,18,36. GCF is 12.

Step2: Find GCF of \(a\)-terms

For \(a^{12}\), \(a^4\), \(a^3\), the smallest exponent is 3. So GCF is \(a^3\).

Step3: Find GCF of \(b\)-terms

For \(b^3\), \(b^0\) (since 12\(a^4\) has no \(b\)), \(b^5\), the smallest exponent is 0. So GCF is \(b^0 = 1\).

Step4: Combine results

Multiply GCF of coefficients, \(a\)-terms, and \(b\)-terms: \(12 \times a^3 \times 1 = 12a^3\).

Answer:

\(12a^3\)