Find the GCD for the following:(i) ab2c3, a2b3c, a3bc2 (ii) 35x5y3z4,

1.	Find the GCD for the following:(i) ab2c3, a2b3c, a3bc2 (ii) 35x5y3z4, 49x2yz3, 14xy2z2(iii) 25 ab3c, 100 a2bc, 125 ab (iv) 3abc, 5xyz, 7pqr
Answer» (i) ab²c³, a²b³c, a³bc² ab²c³ = a x b x b x c x c x c a²b³c = a x a x b x b x b x c a³bc² = a x a x a x b x c x c G.C.D. of ab²c³, a²b³c, a³bc² = a x b x c = abc (ii) 35x⁵y³z⁴, 49x²yz3, 14xy²z² 35x⁵y³z⁴ = 5 x 7 x⁵ y³ z⁴ 49x²yz³ = 7 x 7 x² y z³ 14xy² z² = 2 x 7 x y² z² G.C.D. is = 7 x y z² (iii) 25 ab³ c, 100 a² bc, 125 ab 25 ab³ c = 5 x 5 ab³ c 100 a² bc = 2 x 5 x 2 x 5 a² b c 125 ab = 5 x 5 x 5 ab G.C.D is = 5 x 5 ab = 25ab (iv) 3abc, 5xyz, 7pqr 3abc = 1 x 3 a bc 5xyz = 1 x 5 x y z 7pqr = 1 x 7 p q r G.C.D is 1

Find the GCD for the following:(i) ab2c3, a2b3c, a3bc2 (ii) 35x5y3z4, 49x2yz3, 14xy2z2(iii) 25 ab3c, 100 a2bc, 125 ab (iv) 3abc, 5xyz, 7pqr

Answer»

(i) ab²c³, a²b³c, a³bc²

ab²c³ = a x b x b x c x c x c

a²b³c = a x a x b x b x b x c

a³bc² = a x a x a x b x c x c

G.C.D. of ab²c³, a²b³c, a³bc² = a x b x c = abc

(ii) 35x⁵y³z⁴, 49x²yz3, 14xy²z²

35x⁵y³z⁴ = 5 x 7 x⁵ y³ z⁴

49x²yz³ = 7 x 7 x² y z³

14xy² z² = 2 x 7 x y² z²

G.C.D. is = 7 x y z²

(iii) 25 ab³ c, 100 a² bc, 125 ab

25 ab³ c = 5 x 5 ab³ c

100 a² bc = 2 x 5 x 2 x 5 a² b c

125 ab = 5 x 5 x 5 ab

G.C.D is = 5 x 5 ab = 25ab

(iv) 3abc, 5xyz, 7pqr

3abc = 1 x 3 a bc

5xyz = 1 x 5 x y z

7pqr = 1 x 7 p q r

G.C.D is 1