Calculate the Number Defined by Prime Factors 7 and 2

Q: Why do I multiply the prime factors instead of adding them?

Prime factorization means breaking a number into its prime building blocks. To rebuild the original number, you must multiply these blocks together, just like 2 × 7 = 14.

Q: How can I check if 14 is correct?

Divide 14 by its prime factors: $ 14 \div 2 = 7 $ and $ 7 \div 7 = 1 $. Since 7 is prime, we're done!

Q: What makes a number prime?

A prime number has exactly two factors: 1 and itself. Both 2 and 7 are prime because they can't be divided evenly by any other numbers.

Q: Could the answer be a different number with the same prime factors?

No! Each number has a unique prime factorization. Only 14 has exactly the prime factors 2 and 7 (each appearing once).

Prime Factorization with Multiplication Product

What is the number whose prime factors are: $7,2$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find the number with the given prime factors

00:03 To find the number, multiply all the factors together

00:07 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

What is the number whose prime factors are: $7,2$

Step-by-step solution

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).

Final Answer

$14$

Key Points to Remember

Essential concepts to master this topic

Prime Factorization Rule: Multiply all prime factors to find the original number
Technique: For prime factors 2 and 7: $2 \times 7 = 14$
Check: Verify 14 divides only by 1, 2, 7, and 14 itself ✓

Common Mistakes

Avoid these frequent errors

Adding prime factors instead of multiplying
Don't add prime factors like 2 + 7 = 9! Adding gives a completely different number that doesn't have the correct prime factorization. Always multiply prime factors together to reconstruct the original number.

Practice Quiz

Test your knowledge with interactive questions

Write all the factors of the following number: $$ 6 $$

FAQ

Everything you need to know about this question

Why do I multiply the prime factors instead of adding them?

Prime factorization means breaking a number into its prime building blocks. To rebuild the original number, you must multiply these blocks together, just like 2 × 7 = 14.

What if there are repeated prime factors?

Include each repeated factor in your multiplication! For example, if prime factors are 2, 2, and 3, then the number is $2 \times 2 \times 3 = 12$ .

How can I check if 14 is correct?

Divide 14 by its prime factors: $14 \div 2 = 7$ and $7 \div 7 = 1$ . Since 7 is prime, we're done!

What makes a number prime?

A prime number has exactly two factors: 1 and itself. Both 2 and 7 are prime because they can't be divided evenly by any other numbers.

Could the answer be a different number with the same prime factors?

No! Each number has a unique prime factorization. Only 14 has exactly the prime factors 2 and 7 (each appearing once).

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