Question

Find the GCF of the list of terms. 24a⁶,36a⁴and 48a³ ?

Answer 1

The GCF of 24a⁶, 36a⁴, and 48a³ is found by factoring each term into its prime factors and then determining the smallest power of each common factor present in all the terms, which results in 12a³.

Step-by-step explanation:

To find the Greatest Common Factor (GCF) of the given terms 24a⁶, 36a⁴, and 48a³, we need to break each term into its prime factors and then identify the common factors.

• 24a⁶ = 2³ × 3 × a⁶
• 36a⁴ = 2² × 3² × a⁴
• 48a³ = 2⁴ × 3 × a³

Now, let's find the common factors:

• The smallest power of 2 that is present in all terms is 2².
  
• The smallest power of 3 that is present in all terms is 3.
  
• The smallest power of 'a' that is present in all terms is a³.
  

Therefore, the GCF would be the product of these smallest powers, which gives us 2² × 3 × a³ or 12a³.