A florist has 56 roses and 70 carnations to make table centerpieces. He wants to put an equal number of roses and carnations into each centerpiece.
the answer is 2, 7 or 14
2x7 not 2, 7
56 = 7*4*2 = 14*4
70 = 7*5*2 = 14*5
so 14 divides evenly into 56 and 70 ,(just like finding a common factor)
So the florist can make 14 centrepieces, each with 4 roses and 5 carnations.
To determine the number of table centerpieces the florist can make, we need to find a common factor of 56 and 70.
Step 1: Find the prime factorization of 56 and 70.
- The prime factors of 56 are 2 * 2 * 2 * 7 (or 2^3 * 7).
- The prime factors of 70 are 2 * 5 * 7.
Step 2: Identify the common prime factors.
- Both 56 and 70 share the prime factor of 2 and 7.
Step 3: Determine the common factors.
- Count the number of each common prime factor.
- For 2: There are three 2's in the prime factorization of 56, and one 2 in the prime factorization of 70. Therefore, we can only take one 2 into consideration.
- For 7: There is one 7 in the prime factorization of 56, and one 7 in the prime factorization of 70. Therefore, we can take one 7 into consideration.
Step 4: Multiply the common factors.
- Multiplying the common factors gives us 2 * 7 = 14.
Thus, the florist can make 14 table centerpieces using the equal number of roses and carnations.