Solve Word Problems With Gcf Worksheets [PDF] (6.NS.B.4): 6th ... - Free Printable

Problem 1: Football and Basketball Teams

Question:
At Cary Middle School, there are 36 students on the football team and 12 students on the basketball team. No student is on both teams. The athletic director is making identical groups from the two teams, with the same ratio of football and basketball players in each group, with no player left out.

- How many identical groups can the athletic director make?
- How many football players would be in each group?
- How many basketball players would be in each group?

Solution:
To solve this problem, we need to find the greatest common factor (GCF) of the number of football players (36) and basketball players (12). The GCF will tell us the largest number of identical groups that can be formed.

#### Step 1: Find the GCF of 36 and 12
- Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
- Factors of 12: 1, 2, 3, 4, 6, 12
- Common Factors: 1, 2, 3, 4, 6, 12
- Greatest Common Factor (GCF): 12

#### Step 2: Determine the number of groups
The GCF (12) tells us that the athletic director can make 12 identical groups.

#### Step 3: Determine the number of players in each group
- Football players per group: \( \frac{36}{12} = 3 \)
- Basketball players per group: \( \frac{12}{12} = 1 \)

Final Answer for Problem 1:
- Number of identical groups: 12
- Football players per group: 3
- Basketball players per group: 1

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Problem 2: Tomato and Green Bean Plants

Question:
Jerry purchased 45 tomato plants and 9 green bean plants. Jerry will place the plants in identical rows with the same number of tomato plants and the same number of green bean plants in each row. Jerry will make sure to use every plant he has purchased.

- What is the greatest number of identical rows of tomato and green bean plants Jerry can make?
- How many tomato plants will be in one row?
- How many green bean plants will be in a row?

Solution:
To solve this problem, we need to find the greatest common factor (GCF) of the number of tomato plants (45) and green bean plants (9). The GCF will tell us the largest number of identical rows that can be formed.

#### Step 1: Find the GCF of 45 and 9
- Factors of 45: 1, 3, 5, 9, 15, 45
- Factors of 9: 1, 3, 9
- Common Factors: 1, 3, 9
- Greatest Common Factor (GCF): 9

#### Step 2: Determine the number of rows
The GCF (9) tells us that Jerry can make 9 identical rows.

#### Step 3: Determine the number of plants in each row
- Tomato plants per row: \( \frac{45}{9} = 5 \)
- Green bean plants per row: \( \frac{9}{9} = 1 \)

Final Answer for Problem 2:
- Greatest number of identical rows: 9
- Tomato plants per row: 5
- Green bean plants per row: 1

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Problem 3: Lollipops and Chocolate Kisses

Question:
Linda has 77 lollipops and 66 chocolate kisses. She wants to make identical treat bags with the same number of lollipops and the same number of chocolate kisses in each treat bag, with no items left over.

- What is the largest number of bags that Linda can make?
- How many lollipops will be in each bag?
- How many chocolate kisses will be in each bag?

Solution:
To solve this problem, we need to find the greatest common factor (GCF) of the number of lollipops (77) and chocolate kisses (66). The GCF will tell us the largest number of identical bags that can be formed.

#### Step 1: Find the GCF of 77 and 66
- Factors of 77: 1, 7, 11, 77
- Factors of 66: 1, 2, 3, 6, 11, 22, 33, 66
- Common Factors: 1, 11
- Greatest Common Factor (GCF): 11

#### Step 2: Determine the number of bags
The GCF (11) tells us that Linda can make 11 identical bags.

#### Step 3: Determine the number of items in each bag
- Lollipops per bag: \( \frac{77}{11} = 7 \)
- Chocolate kisses per bag: \( \frac{66}{11} = 6 \)

Final Answer for Problem 3:
- Largest number of bags: 11
- Lollipops per bag: 7
- Chocolate kisses per bag: 6

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Final Answers:

1. Problem 1:
- Number of identical groups: 12
- Football players per group: 3
- Basketball players per group: 1

2. Problem 2:
- Greatest number of identical rows: 9
- Tomato plants per row: 5
- Green bean plants per row: 1

3. Problem 3:
- Largest number of bags: 11
- Lollipops per bag: 7
- Chocolate kisses per bag: 6

Boxed Final Answers:
\[
\boxed{
\begin{array}{l}
\text{Problem 1: } 12 \text{ groups, 3 football players/group, 1 basketball player/group} \\
\text{Problem 2: } 9 \text{ rows, 5 tomato plants/row, 1 green bean plant/row} \\
\text{Problem 3: } 11 \text{ bags, 7 lollipops/bag, 6 chocolate kisses/bag}
\end{array}
}
\]