Question

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 1

(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