Final answer:
The common factors of the monomials 7pq and 14p² are 7 and p, which are present in both monomials, with 7 being a prime factor and p being a variable that appears in both terms to at least the first power.
Step-by-step explanation:
To find the common factors of the monomials 7pq and 14p², we look for any numbers or variables that appear in both monomials. Writing down the prime factorization can help us find common factors.
- 7pq can be factored as (7) × (p) × (q).
- 14p² can be factored as (2) × (7) × (p) × (p).
The common factors are 7 and p, since these are the terms that appear in the factorization of both monomials.
To check that our answer is reasonable, we can look at the original monomials and confirm that both include the factors 7 and p. Indeed, the first monomial is once multiplied by 7 and p, while the second monomial is once multiplied by 7 and twice by p, making p a common factor, although it appears to a different exponent in each.