Mary is creating bouquets of flowers using 18 roses,9 lilies, and 21 carnations. She wants each bouquet to be identical with no flowers left over. What is the greatest number of bouquets that Mary can make?
What is the greatest common factor of 18, 9, and 21?
The greatest amount of bouquets you could make is 3 because 3 is the least common factor and it goes into all the numbers equally
To find the greatest number of bouquets Mary can make, we need to determine the common factors of the given numbers (18, 9, 21).
First, let's find the prime factorization of each number:
18 = 2 * 3 * 3
9 = 3 * 3
21 = 3 * 7
Next, we need to find the lowest occurrence of each prime factor, since we need to create identical bouquets:
We have two 2s, two 3s, and one 7.
To find the greatest number of bouquets, we take the lowest occurrence of each prime factor and multiply them together:
2 * 3 * 3 * 7 = 126
Therefore, Mary can create a maximum of 126 bouquets.