Determine the Number from Prime Factors: 3, 2, and 13

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 × 3 × 13 = 78.

Q: Does the order of multiplication matter?

No! You can multiply prime factors in any order due to the commutative property. Whether you do 3 × 2 × 13 or 13 × 3 × 2, you'll get the same answer: 78.

Q: How can I check if my answer is correct?

Work backwards! Take your answer and factor it completely. If you get back the same prime factors listed in the problem, your answer is right.

Q: Are 2, 3, and 13 really all prime numbers?

Yes! A prime number has exactly two factors: 1 and itself. Check: 2 (1,2), 3 (1,3), and 13 (1,13) all qualify as prime numbers.

Prime Factorization with Multiple Prime Numbers

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

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:05 Let's find the number using the given prime factors.

00:09 First, multiply all the factors together.

00:13 Do one multiplication at a time, step by step.

00:18 Break down thirteen into ten plus three, then multiply.

00:29 Let's calculate these multiplications now.

00:38 And there you have it, that's the solution!

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: $3,2,13$

Step-by-step solution

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 $78$ .

Final Answer

$78$

Key Points to Remember

Essential concepts to master this topic

Rule: Multiply all prime factors together to find the original number
Technique: Work step by step: $3 \times 2 = 6$ , then $6 \times 13 = 78$
Check: Verify by factoring 78 back to get 2, 3, and 13 ✓

Common Mistakes

Avoid these frequent errors

Adding prime factors instead of multiplying
Don't add the prime factors like 3 + 2 + 13 = 18! This gives a completely wrong answer because addition doesn't rebuild the original number. Always multiply all prime factors together to find the original number.

Practice Quiz

Test your knowledge with interactive questions

Write all the factors of the following number: $$ 9 $$

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 × 3 × 13 = 78.

Does the order of multiplication matter?

No! You can multiply prime factors in any order due to the commutative property. Whether you do 3 × 2 × 13 or 13 × 3 × 2, you'll get the same answer: 78.

How can I check if my answer is correct?

Work backwards! Take your answer and factor it completely. If you get back the same prime factors listed in the problem, your answer is right.

What if I get confused with larger numbers?

Break it down step by step! Multiply two factors first, then multiply that result by the next factor. For example: $3 \times 2 = 6$ , then $6 \times 13 = 78$ .

Are 2, 3, and 13 really all prime numbers?

Yes! A prime number has exactly two factors: 1 and itself. Check: 2 (1,2), 3 (1,3), and 13 (1,13) all qualify as prime numbers.

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