The H.C.F of $5 x^{2} y^{3}$ and $10 x^{3} y^{2}$ is

10 x^{3} y^{3}

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5 x^{2} y^{2}

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5 x y

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5 x^{3} y^{3}

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Solution

The correct option is B $5 x^{2} y^{2}$
Let $a = 5 x^{2} y^{3}, b = 10 x^{3} y^{2}$
Splitting $a$ and $b$ we get,
$a = 5 \times x \times x \times y \times y \times y$ and $b = 2 \times 5 \times x \times x \times x \times y \times y .$
The common factors in $a$ and $b$ are $5, x, x, y, y$
$∴$ H.C.F(highest common factor) of $a$ and $b$ $= 5 \times x \times x \times y \times y = 5 x^{2} y^{2}$ .

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The H.C.F of 5x2y3 and 10x3y2 is

The correct option is B 5x2y2Let a=5x2y3,b=10x3y2 Splitting a and b we get,a=5×x×x×y×y×y and b=2×5×x×x×x×y×y.The common factors in a and b are 5,x,x,y,y∴ H.C.F(highest common factor) of a and b =5×x×x×y×y=5x2y2.

The H.C.F of $5 x^{2} y^{3}$ and $10 x^{3} y^{2}$ is