A marching band has 36 members. What arrangement could they use in order to have equal numbers of players in each row?
What are the factors of 36?
1,2,3,4,6,12,18,36
These are all factors of 36
To determine the arrangement for having an equal number of players in each row, you need to find the factors or divisors of 36. The factors are the numbers that divide evenly into 36 without a remainder.
To find the factors, you can start by dividing 36 by the smallest prime number, which is 2. If 36 is divisible by 2, then 2 is a factor. In this case, 36 is indeed divisible by 2, and the result is 18.
Now, you take the result, 18, and divide it again by 2. If it's divisible, then 2 is a factor again. The new result is 9.
Next, you divide 9 by 2. Since it's not divisible evenly, move on to the next prime number, 3. Divide 9 by 3, and it gives you 3.
Now you have 3 as the new result. Dividing it by 2 or 3 won't give an even division, so you move on to the next prime number, 5. Since 3 is not divisible by 5, you can stop here.
Therefore, the factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36.
To have an equal number of players in each row, you can arrange the marching band in rows with any of these factors as the number of players in each row. For example, you could have 2 rows of 18, 3 rows of 12, or 4 rows of 9.
Keep in mind, though, that the specific arrangement will depend on any additional constraints or preferences you may have.