FACTORS AND GREATEST COMMON FACTORS WORKSHEET

Problem 1 : 

Write the prime factorization of 60 using factor tree and ladder diagram.

Problem 2 : 

Write the prime factorization of 60 using ladder diagram.

Problem 3 : 

Find the GCF of 24 and 60 using the list of factors. 

Problem 4 : 

Find the GCF of 18 and 27 using prime factorization. 

Problems 5-6 : Find the GCF of each pair of monomials.

Problem 5 : 

3x3 and 6x2

Problem 6 : 

4x2 and 5y3

Problem 7 : 

Joseph is creating a Web page that offers electronic greeting cards. He has 24 special occasion designs and 42 birthday designs. The cards will be displayed with the same number of designs in each row. Special occasion and birthday designs will not appear in the same row. How many rows will there be if Joseph puts the greatest possible number of designs in each row?

Detailed Answer Key

1. Answer : 

Choose any two factors of 60 to begin. Keep finding factors until each branch ends in a prime factor. 

2. Answer :

Choose a prime factor of 60 to begin. Keep dividing by prime factors until the quotient is 1.

3. Answer : 

Factors of 24 : 1, 2, 3, 4, 6, 8, 12, 24 

Factors of 60 : 1234, 5, 6, 10, 12, 15, 20, 30, 60

The GCF of 24 and 60 is 12. 

4. Answer :

18 : 2 3

27 : 3 ⋅ 3

⋅ =  9

The GCF of 18 and 27 is 9. 

5. Answer : 

Write the prime factorization of each coefficient and write powers as products.

3x3  =   3 ⋅ x ⋅ ⋅ x

3x2  =  2 ⋅ ⋅ x ⋅ x

Find the product of the common factors.

⋅ ⋅ x  =  3x2

The GCF of 3x3 and 6x2 is 3x2.

6. Answer : 

Write the prime factorization of each coefficient and write powers as products.

4x2  =  2 ⋅ 2 ⋅ x ⋅ x

5y3  =  5 ⋅ y ⋅ y ⋅ y

There are no common factors other than 1.

The GCF of 4x2 and 5yis 1. 

7. Answer :

The 24 special occasion designs and 42 birthday designs must be divided into groups of equal size. The number of designs in each row must be a common factor of 24 and 42.

Factors of 24 : 123, 4, 6, 8, 12, 24 

Factors of 42 : 1236, 7, 14, 21, 42

The GCF of 24 and 42 is 6.

The greatest possible number of designs in each row is 6. Find the number of rows of each group of designs when there are 6 designs in each row.

24 special occasion designs / 6 designs per row  =  4 rows

42 birthday designs / 6 designs per row  =  7 rows

When the greatest possible number of designs is in each row, there are 11 rows in total.

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