Identifying the Factors of 13: A Prime Number Analysis

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

Factors are all numbers that divide evenly into a given number. Prime factors are the prime numbers that multiply together to make the original number. For 13, the factors are 1 and 13, but since 13 is prime, it has no prime factorization!

Q: How do I know if 13 is really prime?

Test if any number from 2 to $ \sqrt{13} $ (about 3.6) divides into 13 evenly. Since 2 and 3 don't divide 13, it's definitely prime!

Q: Are 1 and 13 both considered factors of 13?

Yes! Every number is divisible by 1 and itself. So 1 and 13 are the complete list of factors for 13.

Q: How is this different from composite numbers?

Composite numbers have more than two factors. For example, 12 has factors 1, 2, 3, 4, 6, and 12. Prime numbers like 13 have exactly two factors.

Q: What if I can't remember if a number is prime?

Use the divisibility test: try dividing by small primes (2, 3, 5, 7...) up to the square root. If none divide evenly, it's prime!

Prime Numbers with Factor Identification

Write all the factors of the following number: $13$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find all prime factors of the number

00:09 It seems that all these factors are not factors of the number

00:20 The number is prime itself

00:23 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

Write all the factors of the following number: $13$

Step-by-step solution

The task is to find all factors of the number $13$ . To solve this, let's go through the steps:

**Step 1: Determine if $13$ is a prime number**

A prime number is defined as a number greater than $1$ that has no divisors other than $1$ and itself. Therefore, a prime number like $13$ will have exactly two factors: $1$ and $13$ itself.

**Step 2: Conclude the factors**

Since $13$ is a prime number, we list its factors:

The factors of $13$ are $1$ and $13$ .

According to the given multiple choices, we identify the congruence:

Choice 4: $13, 1$ which represents the factors of $13$ , making it the correct answer.

Therefore, the correct solution can be concluded as follows:

The factors of $13$ are $1$ and $13$ .

Final Answer

No prime factors

Key Points to Remember

Essential concepts to master this topic

Prime Definition: Numbers greater than 1 with exactly two factors
Factor Finding: Test divisibility by numbers from 2 to $\sqrt{13}$ ≈ 3.6
Verification: Prime numbers have only 1 and themselves as factors ✓

Common Mistakes

Avoid these frequent errors

Confusing factors with prime factorization
Don't look for prime factors when asked for all factors = missing the complete factor list! Prime factorization breaks numbers into prime components, while factors are all numbers that divide evenly. Always list both 1 and the number itself for prime numbers.

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 factors and prime factors?

Factors are all numbers that divide evenly into a given number. Prime factors are the prime numbers that multiply together to make the original number. For 13, the factors are 1 and 13, but since 13 is prime, it has no prime factorization!

How do I know if 13 is really prime?

Test if any number from 2 to $\sqrt{13}$ (about 3.6) divides into 13 evenly. Since 2 and 3 don't divide 13, it's definitely prime!

Why does the correct answer say 'No prime factors'?

This appears to be an error in the question setup. The question asks for all factors, not prime factors. The factors of 13 are 1 and 13. Prime numbers don't have prime factors other than themselves.

Are 1 and 13 both considered factors of 13?

Yes! Every number is divisible by 1 and itself. So 1 and 13 are the complete list of factors for 13.

How is this different from composite numbers?

Composite numbers have more than two factors. For example, 12 has factors 1, 2, 3, 4, 6, and 12. Prime numbers like 13 have exactly two factors.

What if I can't remember if a number is prime?

Use the divisibility test: try dividing by small primes (2, 3, 5, 7...) up to the square root. If none divide evenly, it's prime!

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