Sharon is creating potpourri bowls using 9 bags of shredded bark and 12 bags of flower petals. If she wants to make all the potpourri bowls identical, containing the same number of bags of shredded bark and the same number of bags of flower petals, what is the greatest number of potpourri bowls Sharon can create?
Question
Sharon is creating potpourri bowls using 9 bags of shredded bark and 12 bags of flower petals. If she wants to make all the potpourri bowls identical, containing the same number of bags of shredded bark and the same number of bags of flower petals, what is the greatest number of potpourri bowls Sharon can create?
Solution
To find out the greatest number of potpourri bowls Sharon can create, we need to find the greatest common divisor (GCD) of the number of bags of shredded bark and the number of bags of flower petals. The GCD is the largest number that can divide both numbers without leaving a remainder.
Step 1: List the divisors of each number. The divisors of 9 are: 1, 3, 9. The divisors of 12 are: 1, 2, 3, 4, 6, 12.
Step 2: Identify the common divisors. The common divisors of 9 and 12 are: 1, 3.
Step 3: The greatest common divisor is the largest of these, which is 3.
So, Sharon can create 3 identical potpourri bowls, each with 3 bags of shredded bark and 4 bags of flower petals.
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