Determine the Number with Prime Factors 5 and 11

Q: What exactly are prime factors?

Prime factors are the prime numbers that multiply together to make a larger number. Think of them as the building blocks - you can't break them down any further!

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

When we say "prime factors", we mean the numbers that are multiplied together to create the original number. Adding would give us a sum, not the number we're looking for!

Q: How can I check if 55 really has prime factors 5 and 11?

Divide 55 by each factor: $ 55 ÷ 5 = 11 $ and $ 55 ÷ 11 = 5 $. Since both results are the other prime factor, you know it's correct!

Q: What if there were more than two prime factors?

The same rule applies! Multiply all the prime factors together. For example, if the prime factors were 2, 3, and 5, the number would be $ 2 \times 3 \times 5 = 30 $.

Q: Could any of the other answer choices work?

Let's check! 16 = 2⁴ (only factor 2), 68 = 2² × 17 (factors 2 and 17), 93 = 3 × 31 (factors 3 and 31). Only 55 has exactly 5 and 11 as factors!

Prime Factorization with Two Factors

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

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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

00:03 To find the number, multiply all the factors together

00:06 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: $5,11$

Step-by-step solution

To find the number whose prime factors are $5$ and $11$ , we need to multiply these factors together. Let's do this step by step:

Multiply the prime factors: $5 \times 11$ .

Performing the multiplication, we calculate:

$5 \times 11 = 55$ .

Therefore, the number whose prime factors are $5$ and $11$ is $55$ .

From the choices provided, the correct answer is $55$ , which corresponds to choice 3.

Final Answer

$55$

Key Points to Remember

Essential concepts to master this topic

Definition: Prime factors are the basic building blocks of any number
Method: Multiply all prime factors together: $5 \times 11 = 55$
Verification: Check by dividing 55 by each prime: 55 ÷ 5 = 11, 55 ÷ 11 = 5 ✓

Common Mistakes

Avoid these frequent errors

Adding prime factors instead of multiplying
Don't add the prime factors like 5 + 11 = 16! This gives a completely different number that doesn't have 5 and 11 as factors. 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 exactly are prime factors?

Prime factors are the prime numbers that multiply together to make a larger number. Think of them as the building blocks - you can't break them down any further!

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

When we say "prime factors", we mean the numbers that are multiplied together to create the original number. Adding would give us a sum, not the number we're looking for!

How can I check if 55 really has prime factors 5 and 11?

Divide 55 by each factor: $55 ÷ 5 = 11$ and $55 ÷ 11 = 5$ . Since both results are the other prime factor, you know it's correct!

What if there were more than two prime factors?

The same rule applies! Multiply all the prime factors together. For example, if the prime factors were 2, 3, and 5, the number would be $2 \times 3 \times 5 = 30$ .

Could any of the other answer choices work?

Let's check! 16 = 2⁴ (only factor 2), 68 = 2² × 17 (factors 2 and 17), 93 = 3 × 31 (factors 3 and 31). Only 55 has exactly 5 and 11 as factors!

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