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Find the greatest common factor of these monomials

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Now the greatest common factor of anything is the largest factor that's divisible in

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into both, if we're just talking about pure numbers

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into both numbers, or in this case into both monomials.

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Now we have to be a little bit careful when we talk about

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greatest in the context of algebraic expressions like this because

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it's greatest from the point of view that it includes for the most factors

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for each of these monomials, it's not necessarily the greatest

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possible number because maybe some of these variables can take on negative values

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maybe they are taking on values less than one

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so d squared is actually going to become a smaller number

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but I think, without getting too much into the weeds there

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I think if we just kind of run through the process of it

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you'll understand it a little bit better

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so to find the greatest common factor

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let's just essentially break down the

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each of these numbers into

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what we could call their prime factorization

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but it's kind of a combination of the prime factorization

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of the numeric parts of the number

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plus essentially the factorization of the variable part

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so if we want to write 10, we could say, or if we want to write 10cd squared

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we can rewrite that as the product of the prime factors of 10