In 2004, there were 35 color guard members in the Cavaliers and 40 in the Blue Devils. The two colors will march in rows with the same number of people in each row without mixing the guards together. If the greatest possible number of people are in each row, how many rows will be there be?

To find the greatest possible number of people in each row, we need to find the greatest common divisor (GCD) of the two numbers - 35 and 40. The GCD represents the largest number that divides both numbers evenly.

To find the GCD, we can use the Euclidean algorithm:
1. Divide the larger number (40) by the smaller number (35).
40 ÷ 35 = 1 remainder 5
2. Now, divide the previous divisor (35) by the remainder (5).
35 ÷ 5 = 7 remainder 0

Since the remainder is 0, our last divisor (5) is the GCD of 35 and 40.

Therefore, the greatest possible number of people in each row is 5.

To determine the number of rows, we can divide the total number of color guard members by the number of people in each row.

For the Cavaliers (35 members):
Number of rows = 35 ÷ 5 = 7

For the Blue Devils (40 members):
Number of rows = 40 ÷ 5 = 8

So, there will be 7 rows in the Cavaliers and 8 rows in the Blue Devils.

sfsdf