Determine the Number: Product of Primes 5, 3, 7, and 11

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

The prime factors are the building blocks (like 5, 3, 7, 11), while the actual number is what you get when you multiply them all together (1155). Think of it like ingredients versus the finished recipe!

Q: Do I need to put the prime factors in order?

No! The order doesn't matter when multiplying. $ 5 \times 3 \times 7 \times 11 $ gives the same result as $ 11 \times 7 \times 3 \times 5 $. Multiplication is commutative.

Q: How can I check my multiplication is correct?

Use division! Take your answer (1155) and divide by each prime factor. You should get the other factors as results: 1155 ÷ 5 = 231, then 231 ÷ 3 = 77, etc.

Q: Why are these called 'prime' factors?

Because each factor (5, 3, 7, 11) is a prime number - it can only be divided by 1 and itself. Prime factorization breaks any number down to its most basic building blocks!

Prime Factorization with Product Calculation

What is the number whose prime factors are: $5,3,7,11$

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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

00:08 To find the number, multiply all factors by each other

00:14 Calculate one multiplication at a time and continue

00:56 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: $5,3,7,11$

Step-by-step solution

To solve this problem, we need to find the number whose prime factors are provided as 5, 3, 7, and 11.

Step-by-step solution:

Step 1: Write down the given prime factors: $5, 3, 7,$ and $11$ .
Step 2: Obtain the product of these prime factors.

Let's perform the multiplication:

$5 \times 3 = 15$

$15 \times 7 = 105$

$105 \times 11 = 1155$

The result of multiplying these prime factors together is $1155$ .

Therefore, the number whose prime factors are $5, 3, 7,$ and $11$ is $1155$ .

The correct choice among the given options is:

Choice 4: $1155$

Final Answer

$1155$

Key Points to Remember

Essential concepts to master this topic

Rule: Prime factorization means finding all prime numbers that multiply together
Technique: Multiply all prime factors: $5 \times 3 \times 7 \times 11 = 1155$
Check: Verify by dividing 1155 by each prime factor completely ✓

Common Mistakes

Avoid these frequent errors

Adding prime factors instead of multiplying
Don't add the prime factors like 5 + 3 + 7 + 11 = 26! This gives a completely wrong number that doesn't have the correct prime factorization. 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

What's the difference between prime factors and the actual number?

The prime factors are the building blocks (like 5, 3, 7, 11), while the actual number is what you get when you multiply them all together (1155). Think of it like ingredients versus the finished recipe!

Do I need to put the prime factors in order?

No! The order doesn't matter when multiplying. $5 \times 3 \times 7 \times 11$ gives the same result as $11 \times 7 \times 3 \times 5$ . Multiplication is commutative.

How can I check my multiplication is correct?

Use division! Take your answer (1155) and divide by each prime factor. You should get the other factors as results: 1155 ÷ 5 = 231, then 231 ÷ 3 = 77, etc.

What if some prime factors are repeated?

If a prime appears multiple times (like 2, 2, 3), you still multiply all of them together! For example, prime factors 2, 2, 3 would give $2 \times 2 \times 3 = 12$ .

Why are these called 'prime' factors?

Because each factor (5, 3, 7, 11) is a prime number - it can only be divided by 1 and itself. Prime factorization breaks any number down to its most basic building blocks!

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