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Find the greatest common factor of the given monomials. $27 a 2 b 3 c 2, 9 a b 2 c 2, 18 a 2 b c 2$

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9abc2

9a2b2c

9a2bc

9abc

answer is A.

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Detailed Solution

Given terms:

27 a 2 b 3 c 2, 9 a b 2 c 2, 18 a 2 b c 2

Factorize 27a²b³c²,

27 a 2 b 3 c 2 = 3 × 3 × 3 × a × a × b × b × b × c × c

Factorize 9ab²c²,

9 a b 2 c 2 = 3 × 3 × a × b × b × c × c

Factorize 18a²bc²,
18

a 2 b c 2 = 2 × 3 × 3 × a × a × b × c × c

Multiply the common factors from all three terms to find greatest common factor.

= 3 × 3 × a × b × c × c = 9 a b c 2

Greatest common factor is

9 a b c 2

.
Hence, option 1 is correct.

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