Question

Find the common factors of the terms A)12x, 36 B) 2y, 22xy C)14pq, 28p^2q^2

Answer 1

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

Answer 2

Answer:-

i) 12x = 2 × 2 × 3 × x

36 = 2 × 2 × 3 × 3

The common factors are 2, 2, 3.

And, 2 × 2 × 3 = 12

(ii) 2y = 2 × y

22xy = 2 × 11 × x × y

The common factors are 2, y.

And, 2 × y = 2y

(iii) $\rm{}14pq$ = 2 × 7 × p × q

$\rm{}28p^2q^2$ = 2 × 2 × 7 × p × p × q × q

The common factors are 2, 7, p, q.

And, 2 × 7 × p × q = 14pq

☆Know more☆

• "Factors" are numbers we can multiply together to get another number.

• When we find the factors of two or more numbers, and then find some factors are the same ("common"), then they are the "common factors".