"Question 1 Find the common factors of the terms (i) 12x, 36 (ii) 2y, 22xy (iii) 14pq, 28p^2q^2 (iv) 2x, 3x^2, 4 (v) 6abc, 24ab^2, 12a^2b (vi) 16x^3, −4x^2, 32x (vii) 10pq, 20qr, 30rp (viii) 3x^2y^3, 10x3y^2, 6x^2y^2z
Class 8 Factorisation Page 220"
Answers
Factors:
In a product of two or more expressions each expression is called a factor of the product.
Factorization:
The process of writing a given expression as a product of two or more factors is called factorization.
Factors of a monomial:
The greatest common factor of 2 or more monomials is the largest common monomial. The largest common monomial is a product of the greatest common factor of the numerical Coefficients and the common variables with smallest powers.
==========================================================
Solution:
Firstly We need to convert each of these terms in simple factors forms and then choose the common factors
i)
12x, 36
12x =2×2×3×x
36=2×2×3×3
Common Factor are 2,2,3
2×2×3=12
(ii) 2y, 22xy
2y=2×y
22xy=2×11×y×x
Common factors are 2,y
2×y=2y
(iii) 14 pq, 28 p²q²
14
pq= 2×7×p×q
28 p²q²=2×2×7×p×p×q×q
common factors are 2,7,p,q
=14pq
(iv) 2x, 3x², 4
2x=2×x
3x2=3×x×x
4=2×2
There is no common factor other than one, so common factor= 1
(v) 6 abc, 24ab², 12 a²b
6abc=2×3×a×b×c
24ab²=2×2×2×3×a×b×b
12a²b=2×2×3×a×a×b
Common factors are 2, 3, a, b
=6ab
(vi) 16 x³, – 4x², 32x
16x³=2×2×2×2×x×x×x
-4x²=-2×2×x×x
32x=-2×2×2×2×2×x
Common factors are 2, 2, x
=4x
(vii) 10 pq, 20qr, 30rp
10pq=-2×5×p×q
20qr=-2×2×5×q×r
30rp=-2×3×5×p×r
Common factors are 2,5
=10
(viii) 3x² y³, 10x³ y²,6 x² y²z
3x²y³=3×x×x×y×y×y
10x³y³=2×5×x×x×x×y×y×y
6x²y²z=2×3×x×x×y×y×z
Common factors are x, x, y, y
=x²y²
==========================================================
Hope this will help you....
I know it's too late but still hope it helps
The answers are in the picture below....
Hope it is clear
