# Worksheet: The Greatest Common Factor

Q1:

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

• Afalse
• Btrue

Q2:

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

• Atrue
• Bfalse

Q3:

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

• AThe common factors are , and the GCF is 8.
• BThe common factors are , and the GCF is 56.
• CThe common factors are , and the GCF is 4.
• DThe common factors are , and the GCF is 4.

Q4:

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

• A53
• B51
• C2
• D1

Q5:

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

• Atrue
• Bfalse

Q6:

Can the greatest common factor of two numbers be 1?

• A yes
• B no

Q7:

Benjamin wants to cut three tree trunks into logs of equal lengths. If the lengths of the tree trunks are 12, 27, and 54 feet, determine the length of the longest log that he can cut.

Q8:

Can the greatest common factor of two numbers be the smaller number?

• A yes
• B no

Q9:

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 Inventory Youth Road Mountain 33 42 39
• A3 helmets, Youth: 22 rows, Road: 28 rows, Mountain: 26 rows
• B6 helmets, Youth: 5 rows, Road: 7 rows, Mountain: 6 rows
• C9 helmets, Youth: 3 rows, Road: 4 rows, Mountain: 4 rows
• D3 helmets, Youth: 11 rows, Road: 14 rows, Mountain: 13 rows
• E3 helmets, Youth: 11 rows, Road: 7 rows, Mountain: 13 rows

Q10:

Which pair of numbers has an GCF of 28?

• A27, 66
• B2, 7
• C7, 66
• D28, 84

Q11:

Determine the GCF for the following set of numbers: 6 inches, 5 feet, 12 inches, 8 feet.

Q12:

Determine the GCF for the following set of numbers: 6 inches, 10 feet, 3 inches, 12 feet.

Q13:

Which of the following pairs of numbers have a greatest common factor of 2?

• A24 and 44
• B55 and 61
• C10 and 50
• D54 and 56

Q14:

Can the greatest common factor of two numbers be the larger number?

• A no
• B yes

Q15:

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

• A99
• B54
• C81
• D110