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Answer :
To find the greatest common factor (GCF) of the terms
[tex]$$90x^4y^2,\quad 330x^6y^3,\quad 240x^2y^3,$$[/tex]
we proceed as follows:
1. Coefficients:
The coefficients of the terms are 90, 330, and 240. The greatest common divisor of these three numbers is 30.
2. Variable [tex]\( x \)[/tex]:
The exponents of [tex]\( x \)[/tex] in the three terms are 4, 6, and 2. The common factor for [tex]\( x \)[/tex] is given by the lowest exponent, which is 2. Hence, the common [tex]\( x \)[/tex]-part is [tex]\( x^2 \)[/tex].
3. Variable [tex]\( y \)[/tex]:
The exponents of [tex]\( y \)[/tex] are 2, 3, and 3. The lowest exponent is 2, so the common factor for [tex]\( y \)[/tex] is [tex]\( y^2 \)[/tex].
4. Combine the Results:
Multiplying the GCD of the coefficients with the common variable parts, we have:
[tex]$$
\text{GCF} = 30 \times x^2 \times y^2 = 30x^2y^2.
$$[/tex]
Thus, the greatest common factor of the given terms is
[tex]$$\boxed{30x^2y^2}.$$[/tex]
[tex]$$90x^4y^2,\quad 330x^6y^3,\quad 240x^2y^3,$$[/tex]
we proceed as follows:
1. Coefficients:
The coefficients of the terms are 90, 330, and 240. The greatest common divisor of these three numbers is 30.
2. Variable [tex]\( x \)[/tex]:
The exponents of [tex]\( x \)[/tex] in the three terms are 4, 6, and 2. The common factor for [tex]\( x \)[/tex] is given by the lowest exponent, which is 2. Hence, the common [tex]\( x \)[/tex]-part is [tex]\( x^2 \)[/tex].
3. Variable [tex]\( y \)[/tex]:
The exponents of [tex]\( y \)[/tex] are 2, 3, and 3. The lowest exponent is 2, so the common factor for [tex]\( y \)[/tex] is [tex]\( y^2 \)[/tex].
4. Combine the Results:
Multiplying the GCD of the coefficients with the common variable parts, we have:
[tex]$$
\text{GCF} = 30 \times x^2 \times y^2 = 30x^2y^2.
$$[/tex]
Thus, the greatest common factor of the given terms is
[tex]$$\boxed{30x^2y^2}.$$[/tex]
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