bryan is setting chairs in rows for a graduation ceremony. He has 50 black chairs and 60 white chairs. Each row will have the same number of chairs, and each row will have the same color chair. What is the greatest number of chairs that he can fit in each row? How many rows of each color chair will there be?

10 chairs in each row 5 black rows and 5 white rows

When you list the GCF of 50 and 60 it will give you 10

10 is equal and greater

To find the greatest number of chairs that Bryan can fit in each row, we need to find the greatest common divisor (GCD) of 50 and 60. The GCD is the largest number that divides both numbers without leaving a remainder.

To find the GCD, we can use the Euclidean algorithm:
1. Divide the larger number by the smaller number.
60 ÷ 50 = 1 remainder 10
2. Divide the remainder (10) by the smaller number (50).
50 ÷ 10 = 5 remainder 0

Since the remainder is now 0, we have found that the GCD of 50 and 60 is 10. Therefore, the greatest number of chairs that Bryan can fit in each row is 10.

To determine how many rows of each color chair there will be, we can divide the total number of chairs by the number of chairs in each row for each color.

For the black chairs:
Number of black chairs ÷ Number of chairs in each row = 50 ÷ 10 = 5 rows

For the white chairs:
Number of white chairs ÷ Number of chairs in each row = 60 ÷ 10 = 6 rows

Therefore, Bryan can fit 10 chairs in each row, and there will be 5 rows of black chairs and 6 rows of white chairs.

10 chairs per row: GCF(50,60)