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The greatest common factor of
200 ×3 and
2×300 is
A)
2×3
B)
20 ×30
C)
23 ×100
D)
200 ×300

$3$ . The greatest common factor of $200 \times 3$ and $2 \times 300$ is $\newline$ A) $2 \times 3$ $\newline$ B) $20 \times 30$ $\newline$ C) $23 \times 100$ $\newline$ D) $200 \times 300$

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Simplify rational expressions

Full solution

Q.

3

. The greatest common factor of

200 \times 3

and

2 \times 300

is

\newline

A)

2 \times 3

\newline

B)

20 \times 30

\newline

C)

23 \times 100

\newline

D)

200 \times 300

Prime Factorization: First, let's write down the prime factorization of each number. $\newline$ $200 \times 3 = 2^3 \times 5^2 \times 3$ $\newline$ $2 \times 300 = 2 \times 2^2 \times 3 \times 5^2$
Find Common Factors: Now, we find the common factors in both prime factorizations. $\newline$ The common factors are $2^3$ , $3$ , and $5^2$ .
Calculate GCF: Multiply the common factors to find the GCF. $\newline$ GCF = $2^3 \times 3 \times 5^2$
Match with Options: Calculate the GCF. $\newline$ GCF = $8 \times 3 \times 25$ $\newline$ GCF = $24 \times 25$ $\newline$ GCF = $600$
Match with Options: Calculate the GCF. $\newline$ GCF = $8 \times 3 \times 25$ $\newline$ GCF = $24 \times 25$ $\newline$ GCF = $600$ Now, let's match our GCF with the given options. $\newline$ $600$ is not explicitly listed, but it can be written as $2 \times 300$ , which is option D.

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