Solve the Prime Factor Equation: What Number Multiplies 5, 13, 11, and 7?

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

Prime factorization means breaking a number down into its prime building blocks through multiplication. Just like 12 = 3 × 4, when we have prime factors 5, 13, 11, and 7, we multiply them: $ 5 \times 13 \times 11 \times 7 = 5005 $.

Q: Can I multiply the prime factors in any order?

Yes! The commutative property of multiplication means you can multiply in any order and get the same result. Whether you do $ 5 \times 13 \times 11 \times 7 $ or $ 7 \times 11 \times 5 \times 13 $, you'll always get 5005.

Q: How can I check if 5005 is really the right answer?

Divide 5005 by each prime factor and make sure you get exact whole number results:5005 ÷ 5 = 10011001 ÷ 7 = 143143 ÷ 11 = 1313 ÷ 13 = 1Since we end with 1 and used all prime factors exactly once, 5005 is correct!

Q: Are all the answer choices valid numbers?

While all answer choices are valid numbers, only 5005 has exactly the prime factors 5, 13, 11, and 7. The other choices would have different prime factorizations when broken down completely.

Prime Factorization with Multiple Prime Numbers

What is the number whose prime factors are: $5,13,11,7$

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Step-by-step video solution

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00:00 Find the number with the given prime factors

00:05 To find the number, multiply all the factors by each other

00:12 Calculate one multiplication at a time and continue

00:27 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: $5,13,11,7$

Step-by-step solution

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: $5005$ .

Final Answer

$5005$

Key Points to Remember

Essential concepts to master this topic

Prime Factors: Each prime appears exactly once in the multiplication
Technique: Multiply sequentially: $5 \times 13 = 65$ , then $65 \times 11 = 715$ , then $715 \times 7 = 5005$
Check: Verify by dividing 5005 by each prime factor to confirm exact division ✓

Common Mistakes

Avoid these frequent errors

Adding instead of multiplying prime factors
Don't add the prime factors like 5 + 13 + 11 + 7 = 36! This gives a completely wrong result because prime factorization means the number is the PRODUCT of its prime factors. 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: $$ 6 $$

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 down into its prime building blocks through multiplication. Just like 12 = 3 × 4, when we have prime factors 5, 13, 11, and 7, we multiply them: $5 \times 13 \times 11 \times 7 = 5005$ .

Can I multiply the prime factors in any order?

Yes! The commutative property of multiplication means you can multiply in any order and get the same result. Whether you do $5 \times 13 \times 11 \times 7$ or $7 \times 11 \times 5 \times 13$ , you'll always get 5005.

How can I check if 5005 is really the right answer?

Divide 5005 by each prime factor and make sure you get exact whole number results:

5005 ÷ 5 = 1001
1001 ÷ 7 = 143
143 ÷ 11 = 13
13 ÷ 13 = 1

Since we end with 1 and used all prime factors exactly once, 5005 is correct!

What if I make a calculation error while multiplying?

Take your time with each step! Multiply two numbers at a time: first $5 \times 13 = 65$ , then $65 \times 11 = 715$ , finally $715 \times 7 = 5005$ . Double-check each multiplication before moving to the next step.

Are all the answer choices valid numbers?

While all answer choices are valid numbers, only 5005 has exactly the prime factors 5, 13, 11, and 7. The other choices would have different prime factorizations when broken down completely.

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