14. (6 points) Pleasant Goat opens a book and finds that the product of the page numbers on the left and right pages is 420. Then the sum of these two page numbers is $\qquad$
【Analysis】Since the page numbers on the left and right pages are two consecutive natural numbers, we first factorize 420 into prime factors, and then form the product of two adjacent factors: $420=2 \times 2 \times 3 \times 5 \times 7=20 \times 21$, so the sum of the page numbers of the two pages is $20+21$ $=41$; thus, the solution is as follows.

【Solution】Solution: According to the fact that the page numbers on the left and right pages are two consecutive natural numbers, we have
$$
420=2 \times 2 \times 3 \times 5 \times 7=20 \times 21 \text {, }
$$

Therefore, the sum of the page numbers of the two pages is: $20+21=41$.
Hence, the answer is: 41.
【Comment】This problem examines the comprehensive application of integer decomposition and page number problems, the key is to find two adjacent factors through prime factorization.