find the greatest common factor of these two expression 18 u^2 v^5 w^3 and 30 u^7 w^4

What is the biggest number that will go into both 18 and 30? Is it 6?

the greatest common factor for variables with exponents is the variable with the smallest power.

for the u's the gcf would be u^2
for v^5 none because the second expression doesn't have a v.

for the w's can you figure it out?

Now, can you put it all together to find the GCF?

i tried.

I'm the only one here in 2020?????



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To find the greatest common factor (GCF) of two expressions, we need to identify the common factors and determine the highest power of each factor that appears in both expressions.

Let's break down the two expressions into their prime factors:

Expression 1: 18u^2v^5w^3
Prime factors of 18: 2 * 3 * 3
Prime factors of u^2: u * u
Prime factors of v^5: v * v * v * v * v
Prime factors of w^3: w * w * w

So, we can rewrite expression 1 as: 2 * 3 * 3 * u * u * v * v * v * v * v * w * w * w

Expression 2: 30u^7w^4
Prime factors of 30: 2 * 3 * 5
Prime factors of u^7: u * u * u * u * u * u * u
Prime factors of w^4: w * w * w * w

So, we can rewrite expression 2 as: 2 * 3 * 5 * u * u * u * u * u * u * u * w * w * w * w

Now, let's compare the common factors in both expressions:

Common factors: 2, 3, u, w

The highest power of each common factor is:
2: occurs once in expression 1 and expression 2
3: occurs once in expression 1 and expression 2
u: occurs twice in expression 1 and seven times in expression 2. The smallest power in both expressions is two, which means it can be the highest power.
w: occurs three times in expression 1 and four times in expression 2. The smallest power in both expressions is three, which means it can be the highest power.

Therefore, the GCF of the two expressions is 2 * 3 * u^2 * w^3, which simplifies to 6u^2w^3.