13. (14 points) To welcome the "World Women's Conference", a school has formed a ceremonial guard consisting of 48 boys and 32 girls. They need to be arranged in $n$ rows $(n>1)$, with the number of boys and girls in each row being equal. How many different ways can they be arranged? How many boys and girls are there in each row for each arrangement?
13. (14 points) To welcome the "World Women's Conference", a school has formed a ceremonial team consisting of 48 boys and 32 girls. They need to be arranged into $n$ rows $(n>1)$, with the number of boys and girls in each row being equal. How many different arrangements are possible? How many boys and girls are there in each row for each arrangement?
【Solution】Solution: The common divisors of 48 and 32 are $2, 4, 8, 16$. Therefore, there are 4 possible arrangements:
(1) Arrange in 2 rows: Each row has 24 boys and 16 girls;
(2) Arrange in 4 rows: Each row has 12 boys and 8 girls;
(3) Arrange in 8 rows: Each row has 6 boys and 4 girls;
(4) Arrange in 16 rows: Each row has 3 boys and 2 girls;
Answer: There are 4 possible arrangements. When arranged in 2 rows, each row has 24 boys and 16 girls; when arranged in 4 rows, each row has 12 boys and 8 girls; when arranged in 8 rows, each row has 6 boys and 4 girls; when arranged in 16 rows, each row has 3 boys and 2 girls.