Question

Art Supplies To celebrate a grand opening, the owner of an art supplies store is making free gift bags for customers. The owner has 225 pastel crayons, 75 paintbrushes, and 120 tubes of oil paint. Each gift bag must be identical. What is the greatest number of gift bags the owner can make?

1) Write the prime factorization of each number.

2) What are the common prime factors of the numbers? What is the GCF of the numbers?

3) What does the GCF represent in this situation?

Short answer

(1) Prime Factors of 225 are:3, 3, 5, 5.

Prime Factors of 75 are:3, 5, 5.

Prime Factors of 120 are:2,2,2, 3, 5.

(2)The common factors are: 1, 3, 5, 15

Then the greatest common factor is 15.

(3) The greatest number of identical gift-bags that can be made out of 225 crayons, 75 paintbrushes and 120 tubes of oil paint

Step-by-step solution

1.Step-1 – Apply the concept of Variable

In any expression or equation, the variable is an unknown quantity. It may be any alphabet or any special symbol.

Step-2 – Given information

225 crayons, 75 paintbrushes and 120 tubes of oil paint.

Step-3 – Calculation

To get the Prime Factors of 225, divide 225 by the smallest prime number possible. Then take the result from that and divide that by the smallest prime number. Repeat this process until end up with 1.

This Prime Factorization process creates the Prime Factor Tree of 225. All the prime numbers that are used to divide in the Prime Factor Tree are the Prime Factors of 225. Here is the math to illustrate:

$\begin{array}{l}225÷3=75\\ 75÷3=25\\ 25÷5=5\\ 5÷5=1\end{array}$

Again, all the prime numbers used to divide above are the Prime Factors of 225.

• Thus, the Prime Factors of 225 are:

3, 3, 5, 5.

Repeat the process for the other two numbers.

• The Prime Factors of 75 are:

3, 5, 5.

• The Prime Factors of 120 are:

2, 2, 2, 3, 5.

2.Step-1 – Apply the concept of Variable

In any expression or equation, the variable is an unknown quantity. It may be any alphabet or any special symbol.

Step-2 – Given information

225 crayons, 75 paintbrushes and 120 tubes of oil paint.

Step-3 – Calculation

The factors of 75 are: 1, 3, 5, 15, 25, 75

The factors of 120 are: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120

The factors of 225 are: 1, 3, 5, 9, 15, 25, 45, 75, 225

The common factors are: 1, 3, 5, 15

Then the greatest common factor is 15.

3.Step-1 – Apply the concept of Variable

In any expression or equation, the variable is an unknown quantity. It may be any alphabet or any special symbol.

Step-2 – Given information

225 crayons, 75 paintbrushes and 120 tubes of oil paint.

Step-3 – Calculation

The greatest common factor here represents the greatest number of identical gift-bags that can be made out of 225 crayons, 75 paintbrushes and 120 tubes of oil paint.