The middle school band has 56 members. The high school band has 96 members. the bands are going to march one after the other in a parade. the director wants to arrange the bands into the same number of columns. What is the greatest number of columns in which the two bands can be arranged if each column has the same number of marchers? how many band members will be in each column? Please help answer these 2 questions Thanks

Highest Common Factor of 56 and 96 is 8..

Q1: 8 columns

Q2 :
For middle school band : 7 members in each column
For high school band : 12 members in each column

To find the greatest number of columns in which the two bands can be arranged, we need to find the greatest common divisor (GCD) of the two numbers: 56 and 96.

To calculate the GCD of two numbers, we can use the Euclidean algorithm. Here's how it works:

1. Divide the larger number by the smaller number: 96 ÷ 56 = 1 remainder 40.
2. Divide the smaller number (56) by the remainder (40): 56 ÷ 40 = 1 remainder 16.
3. Divide the remainder (40) by the new remainder (16): 40 ÷ 16 = 2 remainder 8.
4. Repeat this process until the remainder becomes zero: 16 ÷ 8 = 2 remainder 0.

Since the remainder is zero, the previous remainder (8) is the greatest common divisor (GCD) of 56 and 96. Therefore, the greatest number of columns in which the two bands can be arranged is 8.

To calculate how many band members will be in each column, we need to divide the total number of members in each band by the number of columns.

For the middle school band (with 56 members): 56 ÷ 8 = 7 members per column.
For the high school band (with 96 members): 96 ÷ 8 = 12 members per column.

So, in each column, there will be 7 members from the middle school band and 12 members from the high school band.

What is the greatest common factor of 56 and 96?