Cy has 42 baseball cards and 70 football cards that he wants to group into packages. Each package will have the same number of cards and each package will have the same numbers of baseball cards and football cards. How many packages will Cy make if he uses all of the cards
the greatest common factor (GCF) of 42 and 70 is 14
42 / 14 = 3 ... 70 / 14 = 5
14 packages ... each containing 5 football cards and 3 baseball cards
8? Right
To find out how many packages Cy can make with his baseball and football cards, we need to find a common factor of both numbers.
First, let's find the factors of 42:
1, 2, 3, 6, 7, 14, 21, 42
And the factors of 70:
1, 2, 5, 7, 10, 14, 35, 70
We are looking for the highest common factor (also known as the greatest common divisor or GCD) that is common to both lists. In this case, the highest common factor of 42 and 70 is 14 (since it is the largest number that appears on both lists).
So, Cy can make packages of 14 cards each. The total number of packages he can make is determined by dividing the total number of cards (112) by the number of cards in each package (14):
Total number of cards ÷ Number of cards per package = Number of packages
112 ÷ 14 = 8
Therefore, Cy can make 8 packages with his baseball and football cards.