Question

question
identify the greatest common factor of 30 and 42bc.
answer attempt 1 out of 2

Explanation:

Step1: Factorize 30

To find the factors of 30, we can write it as a product of its prime factors.
We know that \(30 = 2\times3\times5\).

Step2: Factorize 42bc

Now, factorize 42bc. First, factorize 42 into its prime factors.
\(42=2\times3\times7\), and then we have the variables \(b\) and \(c\) which are already in their simplest form (assuming \(b\) and \(c\) are prime or we are only considering the numerical and common variable factors here, but since 30 has no \(b\) or \(c\) factors, we will focus on the numerical part for the GCF of the entire terms).

Step3: Find common factors

Now, find the common prime factors between 30 and 42.
The prime factors of 30 are 2, 3, 5 and the prime factors of 42 are 2, 3, 7. The common prime factors are 2 and 3.

Step4: Calculate GCF

To find the greatest common factor, we multiply the common prime factors.
So, \(2\times3 = 6\). Also, since 30 has no variables (\(b\) or \(c\)) and 42bc has \(b\) and \(c\), but the GCF of the entire terms (30 and 42bc) will only consider the common factors of the numerical part and the common variable factors (but since 30 has no \(b\) or \(c\), the variable part of GCF is 1 for \(b\) and \(c\)). But when we talk about GCF of 30 (a constant) and 42bc (a term with variables), we look at the GCF of the coefficients and the GCF of the variables. The GCF of the coefficients 30 and 42 is 6, and the GCF of the variables (since 30 has no variables, the GCF of variables is 1 for \(b\) and \(c\)). But in terms of the entire expression, the GCF of 30 and 42bc is the GCF of their coefficients (because 30 has no \(b\) or \(c\)) which is 6.

Answer:

6