Find the common factors of the given terms(i) 12x, 36(ii) 14pq, 28p2q2

1.	Find the common factors of the given terms(i) 12x, 36(ii) 14pq, 28p2q2(iii) 6abc, 24ab2, 12a2b(iv) 16x3, – 4x2, 32x(v) 10pq, 20qr, 30rp(vi) 3x2y3, 10x2y2, 6x2y2z
Answer» (i) 12x, 36 12x = 2 × 2 × 3 × x 36 = 2 × 2 × 3 × 3 ∴ Common factor = 2 × 2 × 3 = 12 (ii) 14pq, 28p²q² 14pq = 2 × 7 × p × q 28p²q² = 2 × 2 × 1 × p × p × q × q ∴ Common factor = 2 × 7 × p × q = 14pq (iii) 6abc, 24ab², 12a²b 6abc = 2 × 3 × a × b × c 24 ab² = 2 × 2 × 2 × 3 × a × b × b 12 a²b = 2 × 2 × 3 × a × a × b ∴ Common factor = 2 × 3 × a × b = 6ab (iv) 16x³, – 4x², 32x 16x³ = 2 × 2 ×2 × 2 × x × x × x – 4x² = (- 1) × 2 × 2 × x × x 32x = 2 × 2 × 2 × 2 × 2 × x ∴ Common factor = 2 × 2 × x = 4x (v) 10pq, 20qr, 30rp 10pq = 2 × 5 × p × q 20qr = 2 × 2 × 5 × q × r 30rp = 2 × 3 × 5 × r × p ∴ Common factor = 2 × 5 = 10 (vi) 3x²y³, 10x²y², 6x²y²z 3x²y³ = 3 × x × x × y × y × y 10x²y² = 2 × 5 × x × x × y × y 6x²y²z = 2 × 3 × x × x × y × y × z ∴ Common factor = x × x × y × y = x²y²

Find the common factors of the given terms(i) 12x, 36(ii) 14pq, 28p2q2(iii) 6abc, 24ab2, 12a2b(iv) 16x3, – 4x2, 32x(v) 10pq, 20qr, 30rp(vi) 3x2y3, 10x2y2, 6x2y2z

Answer»

(i) 12x, 36

12x = 2 × 2 × 3 × x

36 = 2 × 2 × 3 × 3

∴ Common factor = 2 × 2 × 3 = 12

(ii) 14pq, 28p²q²

14pq = 2 × 7 × p × q

28p²q² = 2 × 2 × 1 × p × p × q × q

∴ Common factor = 2 × 7 × p × q = 14pq

(iii) 6abc, 24ab², 12a²b

6abc = 2 × 3 × a × b × c

24 ab² = 2 × 2 × 2 × 3 × a × b × b

12 a²b = 2 × 2 × 3 × a × a × b

∴ Common factor = 2 × 3 × a × b = 6ab

(iv) 16x³, – 4x², 32x

16x³ = 2 × 2 ×2 × 2 × x × x × x

– 4x² = (- 1) × 2 × 2 × x × x

32x = 2 × 2 × 2 × 2 × 2 × x

∴ Common factor = 2 × 2 × x = 4x

(v) 10pq, 20qr, 30rp

10pq = 2 × 5 × p × q

20qr = 2 × 2 × 5 × q × r

30rp = 2 × 3 × 5 × r × p

∴ Common factor = 2 × 5 = 10

(vi) 3x²y³, 10x²y², 6x²y²z

3x²y³ = 3 × x × x × y × y × y

10x²y² = 2 × 5 × x × x × y × y

6x²y²z = 2 × 3 × x × x × y × y × z

∴ Common factor = x × x × y × y = x²y²