Identifying All Factors of the Number 8

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

Factors are all numbers that divide evenly into 8: 1, 2, 4, 8. Prime factors are only the prime numbers used in multiplication: 2, 2, 2. Prime factorization shows how to build the number using primes!

Q: Why do I write 2 three times instead of 2³?

Both are correct! $ 2, 2, 2 $ shows each individual prime factor, while $ 2^3 $ uses exponent notation. The question asks for factors, so listing them separately is clearest.

Q: Is 1 considered a prime factor?

No! The number 1 is neither prime nor composite. Prime numbers must have exactly two factors: 1 and themselves. Since 1 only has one factor (itself), it's not prime.

Prime Factorization with Repeated Factors

Write all the factors of the following number: $8$

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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

00:04 The ones digit is 8, therefore 2 is definitely a prime factor

00:08 Divide by 2, and continue with the result to find the factors

00:11 The ones digit is 4, therefore 2 is definitely a prime factor

00:16 Divide by 2, and continue with the result to find the factors

00:19 The result is a prime number, therefore it's a factor by itself

00:22 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: $8$

Step-by-step solution

To find the factors of 8, we'll use prime factorization.

Step 1: Begin with the smallest prime number, 2.
Step 2: Divide 8 by 2, which gives 4. Since 4 is even, divide by 2 again.
Step 3: Divide 4 by 2, which gives 2. Divide 2 by 2 one more time.
Step 4: This yields 1, so we've fully factored the number.

Thus, the prime factorization of 8 is $2 \times 2 \times 2$ .

The factors of the number 8 are $2, 2, 2$ .

Therefore, the correct answer is choice 4: $2, 2, 2$ .

Final Answer

$2,2,2$

Key Points to Remember

Essential concepts to master this topic

Definition: Prime factors are the prime numbers that multiply together
Method: Divide by 2: 8÷2=4, 4÷2=2, 2÷2=1
Check: Multiply prime factors back: 2×2×2 = 8 ✓

Common Mistakes

Avoid these frequent errors

Confusing prime factors with all factors
Don't list all factors like 1, 2, 4, 8 when asked for prime factorization = wrong answer type! Prime factorization only includes the prime numbers that multiply to make the original number. Always write the prime numbers that divide evenly: 2, 2, 2.

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 8: 1, 2, 4, 8. Prime factors are only the prime numbers used in multiplication: 2, 2, 2. Prime factorization shows how to build the number using primes!

Why do I write 2 three times instead of 2³?

Both are correct! $2, 2, 2$ shows each individual prime factor, while $2^3$ uses exponent notation. The question asks for factors, so listing them separately is clearest.

How do I know when I'm done factoring?

Stop when you reach 1! Keep dividing by the smallest prime that works. For 8: 8÷2=4, 4÷2=2, 2÷2=1. When you get 1, you've found all prime factors.

What if I can't divide by 2 anymore?

Try the next smallest prime: 3, then 5, then 7, and so on. But for 8, you only need 2 since $8 = 2^3$ . Always start with 2 for even numbers!

Is 1 considered a prime factor?

No! The number 1 is neither prime nor composite. Prime numbers must have exactly two factors: 1 and themselves. Since 1 only has one factor (itself), it's not prime.

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