Find the greatest common factor of each grouping.(8𝑥𝑦+40𝑥)+(6𝑦+30)Copy to scratch pad

To find the greatest common factor (GCF) of each grouping, we need to break down each term into its prime factors.

1. For the first grouping (8𝑥𝑦+40𝑥):

   • The prime factors of 8 are 2, 2, and 2.
   • The prime factors of 𝑥𝑦 are 𝑥 and 𝑦.
   • The prime factors of 40 are 2, 2, 2, and 5.
   • The prime factors of 𝑥 are 𝑥.
   • So, the GCF of 8𝑥𝑦 and 40𝑥 is 2 * 2 * 2 * 𝑥 = 8𝑥.

2. For the second grouping (6𝑦+30):

   • The prime factors of 6 are 2 and 3.
   • The prime factors of 𝑦 are 𝑦.
   • The prime factors of 30 are 2, 3, and 5.
   • So, the GCF of 6𝑦 and 30 is 2 * 3 = 6.

So, the GCF of each grouping is 8𝑥 for the first grouping and 6 for the second grouping.