A 2-column table with 5 rows. Column 1 is labeled Type of flower with entries lilies, daisies, carnations, asters, daffodils. Column 2 is labeled Amount with entries 60, 36, 72, 42, 24.

Question

The florist makes the greatest number of identical arrangements with the carnations and asters. She has 72 carnations and 42 asters. How can she decide how many carnations to place in each arrangement?
Subtract the number of asters from the number of carnations.
Divide the number of carnations by the GCF of 72 and 42.
Find the least common multiple of 72 and 42.
Find the greatest common factor of 72 and 4

Answer 1

To determine how many carnations to place in each arrangement using the number of carnations (72) and asters (42), the florist should divide the number of carnations by the Greatest Common Factor (GCF) of the two quantities.

Here’s a breakdown of the steps:

1. Find the GCF of 72 and 42:

   • The factors of 72 are: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
   • The factors of 42 are: 1, 2, 3, 6, 7, 14, 21, 42
   • The common factors are: 1, 2, 3, 6
   • The greatest common factor is 6.

2. Divide the number of carnations by the GCF:

   • \( 72 \div 6 = 12 \)

So, the correct approach for the florist is to divide the number of carnations (72) by the GCF of 72 and 42 (which is 6). This would indicate she can place 12 carnations in each arrangement.

Therefore, the correct answer is:

• Divide the number of carnations by the GCF of 72 and 42.