If marching bands vary from 21 to 49 players, which number of players can be arranged in the greatest number of rectangles?

the question becomes:

what number has the largest number of pairs of factors.
I think it is either 48 or 36
they have the same number of factor pairs.

1x48
2x24
3x16
4x12
6x8

1x36
2x18
3x12
4x9
6x6

To determine which number of players can be arranged in the greatest number of rectangles, we need to find a number within the given range that has the most factors.

1. Start by determining the factors of each number within the given range.

For 21, the factors are 1, 3, 7, and 21.
For 22, the factors are 1, 2, 11, and 22.
For 23, the factors are 1 and 23.
For 24, the factors are 1, 2, 3, 4, 6, 8, 12, and 24.
...
For 49, the factors are 1, 7, and 49.

2. Count the number of factors for each number.

For 21, there are 4 factors.
For 22, there are 4 factors.
For 23, there are 2 factors.
For 24, there are 8 factors.
...
For 49, there are 3 factors.

3. Identify the number within the given range that has the highest number of factors.

Based on the above calculations, we can see that 24 has the highest number of factors among the numbers within the range of 21 to 49. Therefore, a marching band with 24 players can be arranged in the greatest number of rectangles.

It's worth noting that the number of factors is related to the divisibility of a number and the arrangement of factors can be visualized as rectangles. By finding the number with the most factors, we can determine the number of players that can be arranged in the most rectangles.

maybe

dis bad

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