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Class 8 RD Sharma Solutions – Chapter 7 Factorization – Exercise 7.1
  • Last Updated : 24 Nov, 2020

Question 1. Find (GCF/HCF) of 2x and 12x2

Solution: 

First Prime Factorize each monomial, then find common among them.

Here,

2x2 = 2 * x * x

12x2 = 2* 2 * 3 * x * x



GCF(2x2, 12x2) = 2 * x * x

                          = 2x2

Question 2. Find (GCF/HCF) of 6x3y and 18x2y3

Solution:  

First Prime Factorize each monomial, then find common among them.

Here,

6x3y = 2 * 3 * x * x * x * y

18x2y3 = 2 * 2 * 3 * x * x * y * y * y

GCF(6x3y, 18x2y3) = 2 * 3 * x * x * y



                               = 6x2y

Question 3. Find (GCF/HCF) of 7x, 21x2 and 14xy2

Solution:  

First Prime Factorize each monomial, then find common among them.

Here,

7x = 7 * x

21x2 = 7 * 3 * x * x

14xy2 = 7 * 2 * x * y * y

GCF(7x, 21x2, 14xy2) = 7*x

                                    = 7x

Question 4. Find (GCF/HCF) of 42x2yz and 63x3y2z3

Solution:  



First Prime Factorize each monomial, then find common among them.

Here,

42x2yz = 2 * 3 * 7 * x * x * y * z

63x3y2z3 = 3 * 3 * 7 * x * x * x * y * y * z * z * z

GCF(42x2yz, 63x3y2z3) = 3 * 7 * x * x * y * z

                                       = 21x2yz

Question 5. Find (GCF/HCF) of 12ax2, 6a2x3 and 2a3x5

Solution:  

First Prime Factorize each monomial, then find common among them.

Here,

12ax2 = 2 * 2 * 3 * a * x * x

6a2x3 = 2 * 3 * a * a * x * x * x

2a3x5 = 2 * a * a * a * x * x * x * x * x

GCF(12ax2, 6a2x3,2a3x5) = 2 * a * x * x

                                         = 2ax2

Question 6. Find (GCF/HCF) of 9x2, 15x2y3, 6xy2 and 21x2y2

Solution:  

First Prime Factorize each monomial, then find common among them.

Here,

9x2 = 3 * 3 * x * x

15x2y3 = 3 * 5 * x * x * y * y * y

6xy2 = 2 * 3 * x * y * y

21x2y2 = 3 * 7 * x * x * y * y

GCF(9x2, 15x2y3, 6xy2 and 21x2y2) = 3 * x

                                                           = 3x

Question 7. Find (GCF/HCF) of 4a2b3, -12a3b, 18a4b3

Solution:  

First Prime Factorize each monomial, then find common among them.

Here,

4a2b3 = 2 * 2 * a * a * b * b * b

-12a3b = -1 * 2 * a * a * a * b

18a4b3 = 2 * 3 * 3 * a * a * a * a * b * b * b

GCF(4a2b3, -12a3b, 18a4b3) = 2 * a * a * b

                                              = 2a2b                                                    

Question 8. Find (GCF/HCF) of 6x2y2, 9xy3, 3x3y2

Solution:  

First Prime Factorize each monomial, then find common among them.

Here,

6x2y2 = 2 * 3 * x * x * y * y

9xy3 = 3 * x * y * y * y

3x3y2 = 3 * x * x * x * y * y

GCF(6x2y2, 9xy3, 3x3y2) = 3 * x * y * y

                                        = 3xy2                                           

Question 9. Find (GCF/HCF) of a2b3,  a3b2

Solution:  

First Prime Factorize each monomial, then find common among them.

Here,

a2b3 = a * a * b * b * b

a3b2 = a * a * a * b * b

GCF(a2b3, a3b2) = a * a * b * b

                           = a2b2

Question 10. Find (GCF/HCF) of 36a2b2c4,  54a5c2, 90a4b2c2

Solution:  

First Prime Factorize each monomial, then find common among them.

Here,

36a2b2c4 = 2 * 2 * 3 * 3 * a * a * b * b * c * c * c * c

54a5c2 = 2 * 3 * 3 * 3 * a * a * a * a * a * c * c

90a4b2c2 = 2 * 3 * 3 * 5 * a * a * a * a * b * b * c * c

GCF(36a2b2c4, 54a5c2, 90a4b2c2) = 2 * 3 * 3 * a * a * c * c

                                                      = 18a2c2

Question 11. Find (GCF/HCF) of x3, -yx2

Solution:  

First Prime Factorize each monomial, then find common among them.

Here,

x3 = x * x * x

-yx2 = -1 * y * x * x

GCF(x3, -yx2) = x * x

                       = x2

Question 12. Find (GCF/HCF) of 15a3, -45a2, -150a

Solution:  

First Prime Factorize each monomial, then find common among them.

Here,

15a3 = 3 * 5 * a * a * a

-45a2 = -1 * 3 * 3 * 5 * a *a

-150a = -1 * 2 * 3 * 5 * 5 * a

GCF(15a3, -45a2, -150a) = 3 * 5 * a

                                        = 15a

Question 13. Find (GCF/HCF) of 2x3y2, 10x2y3, 14xy

Solution:  

First Prime Factorize each monomial, then find common among them.

Here,

2x3y2 = 2 * x * x * x * y * y

10x2y3 = 2 * 5 * x * x * y * y * y

14xy = 2 * 7 * x * y

GCF(2x3y2, 10x2y3, 14xy) = 2 * x * y

                                           = 2xy

Question 14. Find (GCF/HCF) of 14x3y5, 10x5y3, 2x2y2

Solution:  

First Prime Factorize each monomial, then find common among them.

Here,

14x3y5 = 2 * 7 * x * x * x * y * y * y * y * y

10x5y3 = 2 * 5 * x * x * x * x * x * y * y * y

2x2y2 = 2 * x * x * y * y

GCF(14x3y5, 10x5y3, 2x2y2) = 2 * x * x * y * y

                                              = 2x2y2

Find the greatest common factor(GCF) of the terms in the following expressions. (Q15 – Q17)

Question 15. 5a4 + 10a3 – 15a2

Solution:

Here, 5a4 = 5 * a * a * a * a

         10a3 = 2 * 5 * a * a * a

         -15a2 = -1 * 3 * 5 * a * a

5a4 + 10a3 – 15a2 = (5 * a * a * a * a) + (2 * 5 * a * a * a) + (-1 * 3 * 5 * a * a)

                            = 5a2(a2 + 2a – 3)

GCF(5a4 + 10a3 – 15a2) = 5a2

Question 16. 2xyz + 3x2y + 4y2

Solution:

Here, 2xyz = 2 * x * y * z

          3x2y = 3 * x * x * y

           4y2 = 2 * 2 * y * y

2xyz + 3x2y + 4y2 = (2 * x * y * z) + (3 * x * x * y) + (4 * y * y)

                             = y(2x + 3x2 + 4y)

GCF(2xyz + 3x2y + 4y2) = y

Question 17. 3a2b2 + 4b2c2 + 12a2b2c2

Solution:

Here, 3a2b2 = 3 * a * a * b * b

          4b2c2 = 2 * 2 * b * b * c * c

          12a2b2c2 = 2 * 2 * 3 * a * a * b * b * c * c

3a2b2 + 4b2c2 + 12a2b2c2 = (3 * a * a * b * b) + (2 * 2 * b * b * c * c) + (2 * 2 * 3 * a * a * b * b * c * c)

                                         = b(3a2b + 4bc2 + 12a2bc2)

GCF(3a2b2 + 4b2c2 + 12a2b2c2) = b  

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