Question

A Gardener has 2 tulip bulb, 45 tomato plants, 108 rose bushes, and 126 herd seedling to plant in the city garden. He want each row of the garden to have the same number of each kind of plant. What is the greatest number of rows that the garden

Answer 1

Answer: $9\ rows$

Step-by-step explanation:

The complete exercise is:"A gardener has 27 tulip bulbs, 45 tomato plants, 108 rose bushes, and 126 herb seedlings to plant in the city garden. He wants each row of the garden to have the same number of each kind of plant. What is the greatest number of rows that the gardener can make if he uses all the plants?"

The first step to solve the exercise is to find the Greatest Common Factor (GCF) between 27, 45, 108 and 126.

You can follow these steps in order to find the GCF:

1. You must decompose 27, 45, 108 and 126into their prime factors:

$27=3*3*3=3^3\\\\45=3*3*5=3^2*5\\\\108=2*2*3*3*3=2^2*3^3\\\\126=2*3*3*7=2*3^2*7$

2. You must multiply the commons with the lowest exponents. Then:

$GCF=3^2\\\\GCF=9$

Therefore, the greatest number of rows that the gardener can make if he uses all the plants is:

$9\ rows$