Determine the Number with Prime Factors 5 and 13

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

Prime factorization means breaking a number down by multiplication, not addition. Since $ 65 = 5 \times 13 $, we reverse this process by multiplying to get back to the original number.

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

Simply 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: How do I know 5 and 13 are actually prime?

A prime number has exactly two factors: 1 and itself. Check: 5 only divides by 1 and 5, and 13 only divides by 1 and 13, so both are prime!

Q: Could the answer be something other than 65?

No! When you have exactly the prime factors 5 and 13, there's only one possible number: $ 5 \times 13 = 65 $. Prime factorization is unique for each number.

Q: What if the question asked for prime factors of 65 instead?

Then you'd work backwards! Divide 65 by small primes: $ 65 ÷ 5 = 13 $, and since 13 is prime, you get the factors 5 and 13.

Prime Factorization with Two Given Factors

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

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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 factors by each other

00:08 Break down 13 into 10 plus 3, and multiply accordingly

00:18 Calculate the products

00:30 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: $5,13$

Step-by-step solution

To solve this problem, we'll follow these steps:

Step 1: Identify the given prime factors, which are 5 and 13.
Step 2: Multiply these prime factors together to find the number.

Now, let's work through each step:
Step 1: We confirm that the prime factors are $5$ and $13$ .

Step 2: Multiply the prime factors:
$5 \times 13 = 65$ .

Therefore, the number whose prime factors are $5$ and $13$ is $65$ .

Final Answer

$65$

Key Points to Remember

Essential concepts to master this topic

Rule: Multiply all prime factors together to find the number
Technique: Calculate $5 \times 13 = 65$ directly
Check: Verify $65 = 5 \times 13$ and both are prime ✓

Common Mistakes

Avoid these frequent errors

Adding prime factors instead of multiplying
Don't add 5 + 13 = 18! This gives a completely different number that doesn't have the correct prime factorization. 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

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

Prime factorization means breaking a number down by multiplication, not addition. Since $65 = 5 \times 13$ , we reverse this process by multiplying to get back to the original number.

What if there were more than two prime factors?

Simply multiply all the prime factors together! For example, if the prime factors were 2, 3, and 5, the number would be $2 \times 3 \times 5 = 30$ .

How do I know 5 and 13 are actually prime?

A prime number has exactly two factors: 1 and itself. Check: 5 only divides by 1 and 5, and 13 only divides by 1 and 13, so both are prime!

Could the answer be something other than 65?

No! When you have exactly the prime factors 5 and 13, there's only one possible number: $5 \times 13 = 65$ . Prime factorization is unique for each number.

What if the question asked for prime factors of 65 instead?

Then you'd work backwards! Divide 65 by small primes: $65 ÷ 5 = 13$ , and since 13 is prime, you get the factors 5 and 13.

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