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You are making bouquets to sell. You have 60 roses, 84 daisies, and 24 lilies. Each bouquet will have the same number of each kind of flower. You want to use all of the flowers. What is the greatest number of bouquets you can make?
4 bouquets
12 bouquets
6 bouquets
24 bouquets
To find the greatest number of bouquets you can make using all the flowers, we need to determine the greatest common divisor (GCD) of the quantities of each type of flower: 60 roses, 84 daisies, and 24 lilies.
1. Find the GCD:
– The prime factorization of 60: ( 2^2 times 3^1 times 5^1 )
– The prime factorization of 84: ( 2^2 times 3^1 times 7^1 )
– The prime factorization of 24: ( 2^3 times 3^1 )
2. Identify the common factors:
– The common prime factors are ( 2^2 ) and ( 3^1 ).
3. Calculate the GCD:
– GCD = ( 2^2 times 3^1 = 4 times 3 = 12 )
So, the greatest number of bouquets you can make is 12 bouquets.
This means you can create 12 bouquets while using all the flowers, with each bouquet containing 5 roses, 7 daisies, and 2 lilies.