The Greatest Common Divisor (GCD) of 20 a^{2} | vedclass

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Question

(B) To find the Greatest Common Divisor $(GCD)$ of $20 a^{2} b$ and $30 a b^{2}$:$1$. Prime factorization of $20 a^{2} b = 2^{2} 	imes 5 	imes a^{2}

Vedclass · Accepted Answer

False

Vedclass · Answer

(B) To find the Greatest Common Divisor $(GCD)$ of $20 a^{2} b$ and $30 a b^{2}$:$1$. Prime factorization of $20 a^{2} b = 2^{2} 	imes 5 	imes a^{2} 	imes b$.$2$. Prime factorization of $30 a b^{2} = 2 	imes 3 	imes 5 	imes a 	imes b^{2}$.$3$. The $GCD$ is the product of the lowest power of each common prime factor:- Common factors are $2, 5, a, b$.- Lowest powers are $2^{1}, 5^{1}, a^{1}, b^{1}$.- $GCD$ $= 2 	imes 5 	imes a 	imes b = 10 ab$.Since $10 ab 
eq 10 a^{2} b^{2}$,the statement is False.

The Greatest Common Divisor $(GCD)$ of $20 a^{2} b$ and $30 a b^{2}$ is $10 a^{2} b^{2}$. State whether this statement is True or False.

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