Worksheet: The Greatest Common Factor

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

Q1:

Find the greatest common factor of 26 and 14.

Q2:

Find the greatest common factor of 63 and 42.

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 8×27+2×8−22×8, without using a calculator.

Q8:

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

  • A 2 , 2 5 , 2 1
  • B 3 , 3 9 , 3 0
  • C 4 4 , 3 7 , 2
  • D 1 9 , 3 4 , 4 6
  • E 4 0 , 2 0 , 2 9

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 2×7×3 and 2×7×3.

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: 7,14,21,28,….

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

Q22:

Find the common factors of 56 and 36 and state the HCF?

  • AThe common factors are 2,4, and the HCF is 4.
  • BThe common factors are 1,2,4, and the HCF is 4.
  • CThe common factors are 1,2,3,4,6,7,8,9,12,14,18,28,36,56, and the HCF is 56.
  • DThe common factors are 1,2,4,8, and the HCF is 8.

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

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