Prime Factorization: Using factors to solve

To solve this problem, we follow these steps:

• Step 1: Understand that the problem specifies the number whose prime factors are $2, \, 3,$ and $5$.
• Step 2: Multiply these prime factors to find the number.
• Step 3: Perform the multiplication of the numbers.

Let's carry out the calculations:
Step 1: We recognize the number must be composed of the factors $2, 3,$ and $5$.
Step 2: Multiply $2 \times 3 = 6$.
Step 3: Multiply this result by $5$: $6 \times 5 = 30$.

Therefore, the number whose prime factors are $2, 3,$ and $5$ is $30$.

To solve this problem, we need to find the number that corresponds to the given prime factors: 7 and 2.

Steps to solve:

• Step 1: Identify the given prime factors, which are $2$ and $7$.
• Step 2: Multiply the prime factors together. In mathematical terms, this is expressed as:
• $2 \times 7 = 14$

Therefore, the solution to the problem is that the number whose prime factors are 7 and 2 is $14$.

The answer is clearly $\boxed{14}$, corresponding to choice (2).

To find the number whose prime factors are $5$ and $11$, we need to multiply these factors together. Let's do this step by step:

• Multiply the prime factors: $5 \times 11$.

Performing the multiplication, we calculate:

$5 \times 11 = 55$.

Therefore, the number whose prime factors are $5$ and $11$ is $55$.

From the choices provided, the correct answer is $55$, which corresponds to choice 3.

To solve this problem, we'll follow these steps:

• Step 1: Identify the given prime factors, which are 5 and 13.
• Step 2: Multiply these prime factors together to find the number.

Now, let's work through each step:
Step 1: We confirm that the prime factors are $5$ and $13$.

Step 2: Multiply the prime factors:
$5 \times 13 = 65$.

Therefore, the number whose prime factors are $5$ and $13$ is $65$.

To solve this problem, we'll follow these steps:

• Step 1: Identify the given prime factors: $7, 11,$ and $2$.
• Step 2: Multiply these prime factors together to find the number.

Now, let's work through each step:

Step 1: The given prime factors are $7, 11,$ and $2$.

Step 2: Multiply the factors together:
First, calculate $7 \times 11 = 77$.
Then, multiply the result by 2: $77 \times 2 = 154$.

Therefore, the solution to the problem is $154$.

To solve this problem, we'll multiply the given prime factors $5, 7,$ and $5$ to determine the original number.

• Step 1: Multiply the prime factors together: $(5 \times 5) \times 7$.
• Step 2: Calculate $5 \times 5$, which equals $25$.
• Step 3: Multiply the result by the remaining prime factor: $25 \times 7 = 175$.

Therefore, the solution to the problem is $175$.

To solve this problem, we'll follow these steps:

• Step 1: Multiply the first two prime factors.
• Step 2: Multiply the result by the third prime factor.

Now, let's work through each step:
Step 1: Multiply 3 by 2:
$3 \times 2 = 6$

Step 2: Multiply the result by 13:
$6 \times 13 = 78$

Therefore, the number whose prime factors are 3, 2, and 13 is $78$.

To solve this problem, we will follow these steps:

• Step 1: Identify the given prime factors of the number, which are 19, 2, and 3.
• Step 2: Multiply these prime factors to find the number.

Let's work through each step:

Step 1: The problem tells us the prime factors of the number are $19, 2,$ and $3$.

Step 2: We will multiply these factors together to find the number:

$19 \times 2 \times 3$

First, multiply $19 \times 2 = 38$.

Next, multiply the result by 3:

$38 \times 3 = 114$

Thus, by multiplying the given prime factors, we find that the number is $114$.

Therefore, the solution to the problem is $114$.

To find the original number from its prime factors, we need to calculate the product of the given prime numbers.

Given prime factors: $13, 2, 3, \text{ and } 5$.

Calculate the product:

• First, multiply $2$ and $3$:
$\quad 2 \times 3 = 6$
• Next, multiply the result by $5$:
$\quad 6 \times 5 = 30$
• Finally, multiply the result by $13$:
$\quad 30 \times 13 = 390$

Thus, the number whose prime factors are $13, 2, 3,$ and $5$ is $\mathbf{390}$.

The correct choice from the given options is : $\mathbf{390}$

To solve this problem, we need to find the number whose prime factors are provided as 5, 3, 7, and 11.

Step-by-step solution:

• Step 1: Write down the given prime factors: $5, 3, 7,$ and $11$.
• Step 2: Obtain the product of these prime factors.

Let's perform the multiplication:

$5 \times 3 = 15$

$15 \times 7 = 105$

$105 \times 11 = 1155$

The result of multiplying these prime factors together is $1155$.

Therefore, the number whose prime factors are $5, 3, 7,$ and $11$ is $1155$.

The correct choice among the given options is:

• Choice 4: $1155$

Let's tackle the problem of finding the number whose prime factors are $2, 5, 11,$ and another $2$.

First, we need to understand what the problem is asking us to find. It describes a number that is completely defined by its prime factors, given by $2, 5, 11,$ and another $2$. Essentially, we are tasked with determining the composite number that results from multiplying these prime factors together.

• Step 1: Identify the given prime factors: $2, 5, 11,$ and another $2$. This means we actually have $2^2 \times 5 \times 11$.
• Step 2: Multiply the factors together to find the original number. We will break down the calculation for clarity:
  • First, calculate $2^2 = 4$.
  • Next, multiply this result by 5: $4 \times 5 = 20$.
  • Finally, multiply the previous result by 11: $20 \times 11 = 220$.

After performing these calculations, we find that the correct number is indeed 220.

Therefore, the solution to the problem is $220$.

To determine the number with the prime factors $5$, $13$, $11$, and $7$, follow these steps:

• Step 1: Multiply the first two prime factors: $5 \times 13 = 65$.
• Step 2: Multiply the result by the next prime factor: $65 \times 11 = 715$.
• Step 3: Multiply the intermediate product by the last prime factor: $715 \times 7 = 5005$.

Each multiplication step ensures we have correctly included all prime factors to find the original number.

Thus, the number whose prime factors are $5$, $13$, $11$, and $7$ is $5005$.

Referring to the provided multiple-choice options, the correct answer is choice 2: $5005$.