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? find the greatest common factor of 72 and 42. subtract the number of asters from the number of carnations. find the least common multiple of 72 and 42.

Explanation:

Step1: Prime factorize the numbers

Prime factorize \(72\) and \(42\).
\(72 = 2\times2\times2\times3\times3\)
\(42=2\times3\times7\)

Step2: Find the greatest common factor

The common prime factors of \(72\) and \(42\) are \(2\) and \(3\).
Multiply the common prime factors: \(2\times3 = 6\)

Answer:

The greatest number of identical arrangements is \(6\), which is the greatest common factor of \(72\) and \(42\).