Which of the following best defines the greatest common factor (GCF) for a list of algebraic terms?

The sum of all common prime factors shared by the terms.

The factor obtained by taking the average of coefficients and combining it with variables raised to the mean of their exponents in each term.

The largest expression that divides every term, found by multiplying all common prime factors and each variable raised to its smallest exponent appearing across the terms.

The product of the highest powers of primes dividing any of the terms, regardless of whether they are common to all terms.