Identify the greatest common factor of 22, a, x, y22axy and 11, b, x11bx.

Answer 1

To find the greatest common factor (GCF) of the expressions \( 22axy \) and \( 11bx \), we will first factor each expression.

1. Factor \( 22axy \):

   • The number 22 can be factored into \( 2 \times 11 \).
   • Therefore, the expression \( 22axy \) can be written as: \[ 22axy = 2 \times 11 \times a \times x \times y \]

2. Factor \( 11bx \):

   • The number 11 is prime, thus its only factors are 1 and 11.
   • Therefore, the expression \( 11bx \) can be written as: \[ 11bx = 11 \times b \times x \]

Now we will identify the GCF by looking for common factors in both expressions:

• The common numerical factor between \( 22axy \) and \( 11bx \) is 11.
• The common variable factor between the two expressions is \( x \), as \( x \) appears in both.

From this, the GCF can be computed as the product of the common numerical and variable factors:

\[ \text{GCF} = 11 \times x \]

Thus, the greatest common factor of \( 22axy \) and \( 11bx \) is:

\[ \boxed{11x} \]