you are creating identical goodie bags for your birthday party using 18 soccer balls and 30 footballs. What is the greatest number of bags you can fill using all the candy?
GCD(18,30) = 6
So, using
18/6 = 3 soccer balls
and 30/6 = 5 footballs
for each bag, you can make 6 bags
To determine the greatest number of bags you can fill using all the candy, you need to find the greatest common divisor (GCD) of the number of soccer balls and footballs.
To find the GCD, you can use the Euclidean algorithm:
1. Start by dividing the larger number (in this case, 30 footballs) by the smaller number (18 soccer balls).
- 30 ÷ 18 = 1 remainder 12
2. Then, divide the divisor (18) by the remainder (12).
- 18 ÷ 12 = 1 remainder 6
3. Continue dividing the divisor by the remainder until you reach a remainder of 0.
- 12 ÷ 6 = 2 remainder 0
4. The GCD is the last non-zero remainder, which in this case is 6.
So, the greatest number of bags you can fill using all the candy is 6.