Find the Unique Number: Prime Factors 13, 2, 3, and 5

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

Prime factorization means breaking a number into factors that multiply together. Think of it like ingredients in a recipe - you need all of them combined to get the original result!

Q: How can I verify my answer is correct?

Divide your answer by each prime factor - you should get no remainder and eventually reach 1. For 390: 390÷2=195, 195÷3=65, 65÷5=13, 13÷13=1 ✓

Q: Does the order of multiplication matter?

No! You can multiply prime factors in any order due to the commutative property. Whether you do 2×3×5×13 or 13×5×2×3, you'll get the same answer: 390.

Q: What if some prime factors appear more than once?

Include each occurrence in your multiplication! For example, if the prime factors were 2, 2, 3, 5, you'd calculate $ 2 \times 2 \times 3 \times 5 = 60 $.

Prime Factorization with Product Reconstruction

What is the number whose prime factors are: $13,2,3,5$

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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

00:05 To find the number, multiply all factors together

00:10 Use the commutative property to arrange it for easier solving

00:16 Calculate one multiplication at a time and continue

00:26 Break down 13 into 10 plus 3, and multiply accordingly

00:39 Calculate the multiplications

00:48 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: $13,2,3,5$

Step-by-step solution

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 : $\mathbf{390}$

Final Answer

$390$

Key Points to Remember

Essential concepts to master this topic

Rule: Prime factorization gives unique factors that multiply to original number
Technique: Multiply all prime factors: $2 \times 3 \times 5 \times 13 = 390$
Check: Verify by dividing 390 by each prime factor completely ✓

Common Mistakes

Avoid these frequent errors

Adding prime factors instead of multiplying
Don't add the prime factors like 2 + 3 + 5 + 13 = 23! This gives a completely different number that doesn't contain the original factors. Always multiply all 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 factors that multiply together. Think of it like ingredients in a recipe - you need all of them combined to get the original result!

What if I get the wrong answer when multiplying?

Double-check your multiplication step by step! Start with the smallest primes: $2 \times 3 = 6$ , then $6 \times 5 = 30$ , finally $30 \times 13 = 390$ .

How can I verify my answer is correct?

Divide your answer by each prime factor - you should get no remainder and eventually reach 1. For 390: 390÷2=195, 195÷3=65, 65÷5=13, 13÷13=1 ✓

Does the order of multiplication matter?

No! You can multiply prime factors in any order due to the commutative property. Whether you do 2×3×5×13 or 13×5×2×3, you'll get the same answer: 390.

What if some prime factors appear more than once?

Include each occurrence in your multiplication! For example, if the prime factors were 2, 2, 3, 5, you'd calculate $2 \times 2 \times 3 \times 5 = 60$ .

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