Question

Paul has 16 fish pictures and 12 deer pictures to display. He wants to arrange the pictures in rows where the same numbers of fish and deer pictures are in each row. What are the possible numbers of rows Paul will need?

A) 1, 2, 3, 4, 6, 8, 12
B) 2, 4, 8
C) 3, 6, 9
D) 2, 3, 6, 12

Answer 1

Paul can arrange his 16 fish and 12 deer pictures in rows with an equal number of each type only in 2, 4, or 8 rows. These numbers are the common divisors of 16 and 12, excluding the number 1.

Step-by-step explanation:

Paul has 16 fish pictures and 12 deer pictures to arrange in rows with the same number of each type in each row. To determine the possible numbers of rows he can have, we need to find the common divisors of 16 and 12. These are the numbers that can divide both 16 and 12 without leaving a remainder, allowing Paul to create rows with an equal number of both kinds of pictures.

The divisors of 16 are 1, 2, 4, 8, 16 and the divisors of 12 are 1, 2, 3, 4, 6, 12. The common divisors between these two sets are therefore 1, 2, 4, and 8. However, since Paul wants to have both deer and fish pictures in each row, we exclude the number 1 because it would mean having only one picture per row, which does not follow the condition of having both kinds of pictures in each row.

Thus, the possible numbers of rows where Paul can have an equal number of fish and deer pictures are 2, 4, 8.