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52a^5b^3 + 4a^2b

1) when finding the gcf, is it per term or for the entire thing?

2) is this prime because it's not factorable?

gcf distributes across all terms

otherwise, why would it be a "common" factor?

this is not prime, because each term is a multiple of a and b

Did you know?

Did you know that when finding the greatest common factor (GCF) of an expression like 52a^5b^3 + 4a^2b, the GCF is determined per term? This means that we find the highest power of each variable that appears in all the terms and include any common numerical coefficients. In this case, the GCF would be 4ab because it is the highest power of "a" that appears in both terms (a^2 in the second term) and the highest power of "b" that appears in both terms (b in the second term). Furthermore, it is important to note that the fact that an expression is not factorable does not necessarily mean it is prime. In fact, 52a^5b^3 + 4a^2b can still be factored by grouping common factors from each term separately. So let's remember to carefully analyze an expression before concluding whether it is prime or not.