Question

Rashi is going to plant 54 oak trees and 27 pine trees. Rashi would like to plant the trees in all rows that have the same number of trees and are made up of only one type of tree. What is the greatest number of trees Rashi can have in each row? What is the total number of rows she needs to plant? [4 MARKS]

Answer 1

Concept: 1 Mark
Steps: 2 Marks
Answer: 1 Mark

We need to understand that if Rashi has to plant the same number of trees of the same type in a row, then the number of trees in each row should be a factor of 54 and 27.
Now, the greatest common factor will give the greatest number of trees Rashi can plant in each row.
The prime factorization of the numbers is given below.

54= 2 $\times$ 3 $\times$ 3 $\times$ 3

27= 3 $\times$ 3 $\times$ 3

So, the HCF will be 3 $\times$ 3 $\times$ 3 = 27

Therefore 27 trees can be planted in each row.
Total number of rows which will be planted = 54 $÷$ 27 + 27$÷$27 = 3