Find the greatest common factor of these two expressions.
I am stuck
20y^4x^2u^2 and 16y^3u^6.
4y^3 u^2
To find the greatest common factor (GCF) of the two expressions 20y^4x^2u^2 and 16y^3u^6, we need to determine the highest power of each variable that appears in both expressions simultaneously.
Let's break down each expression into its prime factors:
20y^4x^2u^2 = 2 * 2 * 5 * y * y * y * y * x * x * u * u
16y^3u^6 = 2 * 2 * 2 * 2 * y * y * y * u * u * u * u * u * u
Now, we can see the common factors between both expressions:
Common factors for 20y^4x^2u^2 and 16y^3u^6 = 2 * 2 * y * y * u * u = 4y^2u^2
Therefore, the greatest common factor (GCF) of 20y^4x^2u^2 and 16y^3u^6 is 4y^2u^2.
To find the GCF in general, you can:
1. Find the prime factorization of each expression.
2. Identify the common factors by looking at the common prime factors with the lowest exponents.
3. Multiply the common factors together to get the GCF.