José is making fruit-filled tart shells for a party. He has 180 raspberries and 72 blueberries. The tarts will each have the same number of berries. Raspberries and blueberries will not be in the same tart. If he puts the greatest possible number of fruits in each tart, how many tarts can he make?
Don't know how many berries you put in each tart. Assuming 6 berries in each tart, 30 raspberries and 12 blueberries.
7 tarts
36 berries per tart
5 tarts with raspberries
2 tarts with blueberries
7 total
To calculate the number of tarts José can make, we need to find the greatest common divisor (GCD) of 180 and 72. The GCD is the largest number that divides both 180 and 72 without leaving a remainder.
To find the GCD, we can use the Euclidean algorithm. We divide the larger number by the smaller number and take the remainder. Then, we divide the smaller number by this remainder and find the new remainder. We continue this process until we reach a remainder of 0.
Let's apply the Euclidean algorithm to find the GCD of 180 and 72:
- Divide 180 by 72: 180 ÷ 72 = 2 with a remainder of 36
- Divide 72 by 36: 72 ÷ 36 = 2 with a remainder of 0
Since we have reached a remainder of 0, the GCD of 180 and 72 is 36.
Therefore, José can make 36 tarts, as each tart will have 36 berries.