# Worksheet: The Greatest Common Factor

In this worksheet, we will practice finding the greatest common factor of two or more numbers by writing all the factors of these numbers.

**Q3: **

Find the greatest common factor of 9 and 14.

**Q4: **

Find the greatest common factor of 21 and 10.

**Q5: **

Find the greatest common factor of 7,15, and 21.

**Q6: **

Find the greatest common factor of 110, 40, and 120.

**Q7: **

By taking out the highest common factor (HCF), find the value of , without using a calculator.

**Q8: **

Which of the following sets of numbers has an HCF that is equal to one of its numbers?

- A
- B
- C
- D
- E

**Q9: **

Which of the following choices represents three numbers whose greatest common factor is 17?

- A102, 204, 510
- B119, 238, 357
- C238, 204, 136
- D357, 306, 204
- E119, 102, 68

**Q10: **

Find the GCF for 16 gallons, 24 gallons, 36 gallons, and 50 gallons.

**Q11: **

Find the GCF of and .

**Q12: **

Find the greatest common factor of 175 and 25.

**Q13: **

Can the greatest common factor of two numbers be 1?

- Ayes
- Bno

**Q14: **

The given table shows the number of helmets a sports store has in its inventory. If the store’s manager wants to display these helmets such that each helmet style is placed in even rows, determine the greatest number of helmets that can be placed in each row for each helmet style, and then determine how many rows of each helmet style there are.

Style | Youth | Road | Mountain |
---|---|---|---|

Inventory | 33 | 42 | 39 |

- A3 helmets, Youth: 11 rows, Road: 7 rows, Mountain: 13 rows
- B3 helmets, Youth: 22 rows, Road: 28 rows, Mountain: 26 rows
- C3 helmets, Youth: 11 rows, Road: 14 rows, Mountain: 13 rows
- D6 helmets, Youth: 5 rows, Road: 7 rows, Mountain: 6 rows
- E9 helmets, Youth: 3 rows, Road: 4 rows, Mountain: 4 rows

**Q15: **

Mr. Michael is organizing his vinyl collection into boxes by genre. Given that he wants to put the same number of vinyls in each of the boxes without mixing genres, determine the largest number of vinyls he can put into one box and the number of boxes needed.

Genre | Rock | Pop | Jazz |
---|---|---|---|

Number of Vinyls | 70 | 95 | 100 |

- A15 vinyls, 54 boxes
- B6 vinyls, 54 boxes
- C5 vinyls, 53 boxes
- D5 vinyls, 54 boxes
- E15 vinyls, 53 boxes

**Q16: **

Determine the GCF of all the numbers in the following list: .

**Q17: **

Which of the following numbers does not share the same greatest common factor with the other three?

- A56
- B45
- C10
- D35

**Q18: **

Find the HCF of 84 and 28.

**Q19: **

A movie club hosted a movie night for students. Given that each student paid the same amount to attend, determine the highest possible cost per student for the movie night, and find how many students attended.

Arrival Time | 5:00 pm to 6:00 pm | 6:00 pm to 7:00 pm | 7:00 pm to 8:00 pm | 8:00 pm to 9:00 pm |
---|---|---|---|---|

Money Collected | $44 | $30 | $34 | $26 |

- A$2, 67
- B$4, 67
- C$2, 134
- D$1, 33
- E$4, 134

**Q20: **

Is the following true or false? The highest common factor of 40 and 30 is 17.

- Afalse
- Btrue

**Q21: **

Is the following true or false? The highest common factor of 86 and 70 is 2.

- Atrue
- Bfalse

**Q23: **

Find the HCF of 63, 90, and 30.

**Q24: **

What is the highest common factor between the two numbers 51 and 53?

- A51
- B2
- C53
- D1

**Q25: **

Determine whether this statement is true or false: The GCF of any two odd numbers is always odd.

- Afalse
- Btrue