GCF word problems

GCF word problems

Key words

Like all good word problems there are key words we can look for when solving greatest common factor word problems. The most common question or phrase you will see is "What is the greatest number...?"

You may also see "what is the largest?" or "what is the maximum?" basically anything synonymous with greatest.

Key words cont.

Another important phrase to look for in word problems is "distributed evenly", or "having nothing left over". This tells us that we are looking for factors that go in evenly!

Multiple Choice

Which word will you NOT see used in GCF word problems?

• Largest

• Greatest

• Least

• Maximum

Let's look at an example!

Lily is creating party favors with stickers and pencils. She has 16 stickers and 12 pencils, and she wants each party favor to include the same combination of pencils and stickers, with none left over. What is the greatest number of party favors she can make?

Examining the problem

• First identify what you are looking for - "greatest number" = Greatest Common Factor

• What are the two numbers you are asked to find the GCF of - 12 and 16

Solve the problem

Use the list method (as shown in the picture) or the prime factorization method to solve.

Now you try!

To encourage public transportation, Riley wants to give some friends envelopes with bus tickets and subway tickets in them. If she has 18 bus tickets and 12 subway tickets to split equally among the envelopes, and wants no tickets left over, what is the greatest number of envelopes Riley can make?

Open Ended

The two numbers I need to find the greatest common factor of are:

Multiple Choice

The GCF of 12 and 18 is:

• 12

• 4

• 2

• 6

Answer:

That means Riley can make 6 envelopes.

With 18 bus tickets and 12 subway tickets she will have 3 bus tickets and 2 subway tickets in each envelope.

Multiple Choice

A choir teacher is dividing 20 sopranos and 8 altos into singing groups. He wants each group to have the same combination of sopranos and altos, with no singers left over. What is the greatest number of groups he can make?

• 4

• 2

• 8

• 10

Multiple Choice

Grace has collected 18 U.S. stamps and 8 international stamps. She wants to display them in identical groups of U.S. and international stamps, with no stamps left over. What is the greatest number of groups Grace can display them in?

• 2

• 4

• 8

• 10

Challenge!

You can also find the GCF of 3 numbers at a time. The method is still the same. Try this one...

Multiple Choice

Oscar needs to ship 14 rock CDs, 12 classical CDs, and 8 pop CDs. He can pack only one type of CD in each box and he must pack the same number of CDs in each box. What is the greatest number of CDs Oscar can pack in each box?

• 6

• 4

• 8

• 2