GREATEST COMMON FACTOR OF MONOMIALS WORKSHEET

Find the greatest common factor of the monomials. 

1)  7x²yz⁴ and 21x²y⁵z³

2)  x²y, x³y and x²y²

3)  25bc⁴d³, 35b²c⁵, and 45c³d

4)  35x⁵y³z⁴, 49x²yz³ and 14xy²z²

5)  x³y² and xyz 

6)  3x²yz and 4x³y³

7)  p²qr , pq²r and pqr²

8)  66a⁴b²c³, 44a³b⁴c² and 24a²b³c⁴

9)  -27p²qr⁵ and 15p³r³

10)  -30x²y²z² and -50x³y³z³

Detailed Answer Key

1. Answer :

7x²yz⁴  =  7 ⋅ x² ⋅ y ⋅ z³ ⋅ z

21x²y⁵z³  = 3 ⋅ 7 ⋅ x² ⋅ y ⋅ y⁴ ⋅ z³

Common factors are shown in blue.

Product of common factors :

=  7 ⋅ x² ⋅ y ⋅ z³

=  7x²yz³

So, the GCF is 7x²yz³.

2. Answer :

x²y  =  x² ⋅ y  

x³y  =  x² ⋅ x ⋅ y  

x²y²  =  x² ⋅ y ⋅ y  

Product of common factors :

=  x² ⋅ y

=  x²y

So, the GCF is x²y.

3. Answer :

25bc⁴d³  =  5 ⋅ 5 ⋅ b ⋅ c³ ⋅ c ⋅ d³

35b²c⁵  =  5 ⋅ 7 ⋅ b²  ⋅ c³ ⋅ c²

45c³d  =  3 ⋅ 3 ⋅ 5 ⋅ c³ ⋅ d

Product of common factors :

=  5 ⋅ c³

=  5c³

So, the GCF is 5c³.

4. Answer :

35x⁵y³z⁴  =  5 ⋅ 7 ⋅ x⁴ ⋅ x ⋅ y² ⋅ y ⋅ z² ⋅ z²

49x²yz³  =  7 ⋅ 7 ⋅ x ⋅ x ⋅ y ⋅ z² ⋅ z

14xy²z²  =  2 ⋅ 7 ⋅ x ⋅ y ⋅ y ⋅ z²

Product of common factors :

=  7 ⋅ x ⋅ y ⋅ z²

=  7xyz²

So, the GCF is 7xyz².

5. Answer :

x³y²  =  x² ⋅ x ⋅ y ⋅ y

xyz  =   x ⋅ y ⋅ z

Product of common factors :

=  x ⋅ y

=  xy

So, the GCF is xy. 

6. Answer :

3x²yz  =  3 ⋅ x² ⋅ y ⋅ z 

4x³y³  =   2 ⋅ 2 ⋅ x² ⋅ x ⋅ y ⋅ y

Product of common factors :

=  x² ⋅ y

=  x²y

So, the GCF is x²y. 

7. Answer :

p²qr  =  p ⋅ p ⋅ q ⋅ r

pq²r  =  p ⋅ q ⋅ q ⋅ r 

pqr²  =  p ⋅ q ⋅ r ⋅ r

Product of common factors :

=  p ⋅ q ⋅ r

=  pqr

So, the GCF is pqr. 

8. Answer :

66a⁴b²c³  =  2 ⋅ 3 ⋅ 11 ⋅ a² ⋅ a² ⋅ b² ⋅ c² ⋅ c

44a³b⁴c²  =  2 ⋅ 2 ⋅ 11 ⋅ a² ⋅ a ⋅ b² ⋅ b² ⋅ c²

24a²b³c⁴  =  2 ⋅ 2 ⋅ 2 ⋅ 3 ⋅ a² ⋅ b² ⋅ b ⋅ c² ⋅ c²

Product of common factors :

=  2 ⋅ a² ⋅ b² ⋅ c²

=  2a²b²c²

So, the GCF is 2a²b²c².

9. Answer :

-27p²qr⁵  =  -1 ⋅ 3² ⋅ 3 ⋅ p² ⋅ q ⋅ r³ ⋅ r²

15p³r³  =  3 ⋅ 5 ⋅ p² ⋅ p ⋅ r³

Product of common factors :

=  3 ⋅ p² ⋅ r³

=  3p²r³

So, the GCF is 3p²r³.

10. Answer :

-30x²y²z²  =  -1 ⋅ 2 ⋅ 3 ⋅ 5 ⋅ x² ⋅ y² ⋅ z²

-50x³y³z³  =  -1 ⋅ 2 ⋅ 5 ⋅ 5 ⋅ x² ⋅ x ⋅ y² ⋅ y ⋅ z² ⋅ z

Product of common factors :

=  -1 ⋅ 2 ⋅ 5 ⋅ x² ⋅ y² ⋅ z²

=  -10x²y²z²

So, the GCF is -10x²y²z².

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