Solve for the Number: Identifying the Product of Prime Factors 2, 3, and 5

Q: What's the difference between prime factors and composite factors?

Prime factors are numbers like 2, 3, 5, 7 that can only be divided by 1 and themselves. Composite factors like 6 or 15 can be broken down further into prime factors.

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

Prime factorization shows how a number is built up through multiplication. When you multiply $ 2 \times 3 \times 5 = 30 $, you're creating the original number from its basic building blocks.

Q: What if I see the same prime factor repeated?

If a prime appears multiple times (like $ 2^2 \times 3 $), multiply it the number of times it appears: $ 2 \times 2 \times 3 = 12 $.

Q: Can a number have different sets of prime factors?

No! The Fundamental Theorem of Arithmetic says every number has exactly one unique set of prime factors (except for order). 30 will always equal $ 2 \times 3 \times 5 $.

Prime Factorization with Product Calculation

What is the number whose prime factors are: $2,3,5$

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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 factors by each other

00:08 Calculate one multiplication at a time and continue

00:12 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: $2,3,5$

Step-by-step solution

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 $30$ .

Final Answer

$30$

Key Points to Remember

Essential concepts to master this topic

Rule: Prime factors multiply together to create the original number
Technique: Multiply systematically: $2 \times 3 = 6$ , then $6 \times 5 = 30$
Check: Factor 30 back to verify: $30 = 2 \times 3 \times 5$ ✓

Common Mistakes

Avoid these frequent errors

Adding prime factors instead of multiplying
Don't add the prime factors like 2 + 3 + 5 = 10! This gives a completely different number that doesn't have the correct prime factorization. Always multiply prime factors together to find 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

What's the difference between prime factors and composite factors?

Prime factors are numbers like 2, 3, 5, 7 that can only be divided by 1 and themselves. Composite factors like 6 or 15 can be broken down further into prime factors.

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

Prime factorization shows how a number is built up through multiplication. When you multiply $2 \times 3 \times 5 = 30$ , you're creating the original number from its basic building blocks.

What if I see the same prime factor repeated?

If a prime appears multiple times (like $2^2 \times 3$ ), multiply it the number of times it appears: $2 \times 2 \times 3 = 12$ .

How can I check if my answer is correct?

Factor your answer back into primes! For 30: divide by 2 to get 15, divide 15 by 3 to get 5, and 5 is prime. So $30 = 2 \times 3 \times 5$ ✓

Can a number have different sets of prime factors?

No! The Fundamental Theorem of Arithmetic says every number has exactly one unique set of prime factors (except for order). 30 will always equal $2 \times 3 \times 5$ .

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