Malachi collects baseball cards. He has 24 Cincinnati Reds cards and 30 Atlanta Braves cards. The teams are playing each other and Malachi wants to sell sets of his cards. He wants them to have an equal number of each kind in the package. What is the greatest number of packages Malachi can make if he uses all of the cards? PAR 6.2
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1 point
2
3
6
9
To find the greatest number of packages Malachi can make, we need to determine the greatest common divisor (GCD) of 24 and 30.
Prime factorization of 24: 2^3 * 3
Prime factorization of 30: 2 * 3 * 5
The GCD is found by taking the lowest exponent for each common prime factor. In this case, the GCD is 2^1 * 3^1 = 6.
Therefore, the greatest number of packages Malachi can make is 6.
To find the greatest number of packages Malachi can make with equal numbers of each type of card, we need to find the greatest common divisor (GCD) of 24 and 30.
1. First, we list out the factors of 24: 1, 2, 3, 4, 6, 8, 12, and 24.
2. Then, we list out the factors of 30: 1, 2, 3, 5, 6, 10, 15, and 30.
3. The numbers that appear in both lists are: 1, 2, 3, and 6.
4. Therefore, the greatest common divisor of 24 and 30 is 6.
Since 6 is the greatest common divisor, Malachi can make sets of 6 cards (3 Cincinnati Reds and 3 Atlanta Braves) with his collection.
Answer: The greatest number of packages Malachi can make is 6.
To find the greatest number of packages Malachi can make, we need to find the greatest common divisor (GCD) of 24 and 30. 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 (30) by the smaller number (24).
30 ÷ 24 = 1 remainder 6
2. Divide the remainder (6) by the previous divisor (24).
24 ÷ 6 = 4 remainder 0
Since the remainder is 0, we can stop here. The divisor at this step (6) is the GCD of 24 and 30.
Therefore, the greatest number of packages Malachi can make is 6.