Question
Find the greatest common factor of these two expressions. 24v^7w^2 and 14u^6v^4w^5 square
Solution
4.5
(181 Votos)
Leandro
Especialista · Tutor por 3 anos
Resposta
The greatest common factor of
and
is
.
Explicação
## Step 1The greatest common factor (GCF) of two or more numbers or algebraic expressions is the largest number or expression that divides evenly into each of them. In this case, we are asked to find the GCF of
and
.## Step 2First, we need to break down each term into its prime factors. The prime factorization of 24 is
, and the prime factorization of 14 is
. ## Step 3Next, we look at the variables. The variable
appears in both terms, with powers of 7 and 4. The GCF of these powers is
, because 4 is the smaller of the two powers. ## Step 4Similarly, the variable
appears in both terms, with powers of 2 and 5. The GCF of these powers is
, because 2 is the smaller of the two powers. ## Step 5Therefore, the GCF of
and
is
, which simplifies to
.