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What is the greatest common factor of the terms [tex]$14c^2d$[/tex] and [tex]$42c^3d$[/tex]?

A. [tex][tex]$3c$[/tex][/tex]
B. [tex]$7c^2d$[/tex]
C. [tex]$14m^2d$[/tex]
D. [tex][tex]$2c^2d$[/tex][/tex]


Sagot :

To find the greatest common factor (GCF) of the terms [tex]\(14 c^2 d\)[/tex] and [tex]\(42 c^3 d\)[/tex], we can break down the problem into several steps:

1. Determine the GCF of the numerical coefficients:
- The coefficients are 14 and 42.
- The Greatest Common Factor of 14 and 42 is 14.

2. Determine the GCF of the variable [tex]\(c\)[/tex]:
- The first term has [tex]\(c^2\)[/tex].
- The second term has [tex]\(c^3\)[/tex].
- The GCF is the variable raised to the lowest power present in both terms. So, for [tex]\(c\)[/tex], the GCF is [tex]\(c^2\)[/tex].

3. Determine the GCF of the variable [tex]\(d\)[/tex]:
- Both terms have [tex]\(d\)[/tex] to the power of 1.
- Since the exponent for [tex]\(d\)[/tex] is the same in both terms, the GCF is [tex]\(d\)[/tex].

Combining these factors, the GCF of [tex]\(14 c^2 d\)[/tex] and [tex]\(42 c^3 d\)[/tex] is:

[tex]\[ 14 c^2 d \][/tex]

So, the correct choice is:
[tex]\[ \boxed{14 c^2 d} \][/tex]