Discover the Factors of 16: A Fundamental Math Exercise

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

Factors are all numbers that divide evenly into 16: 1, 2, 4, 8, 16. Prime factors are only the prime numbers that multiply together to make 16: 2, 2, 2, 2.

Q: What if I start with a different prime number?

Always start with the smallest prime that divides your number. For even numbers like 16, start with 2. This ensures you find all prime factors systematically.

Q: Can 1 be a prime factor?

No! The number 1 is not prime because it only has one factor (itself). Prime numbers must have exactly two factors: 1 and themselves.

Prime Factorization with Perfect Powers

Write all the factors of the following number: $16$

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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 6, therefore 2 is definitely a prime factor

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

00:12 The ones digit is 8, therefore 2 is definitely a prime factor

00:15 Divide by 2, and continue with the result to find the factors

00:19 The ones digit is 4, therefore 2 is definitely a prime factor

00:22 Divide by 2, and continue with the result to find the factors

00:25 The result is a prime number, therefore it's a factor by itself

00:29 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: $16$

Step-by-step solution

To solve this problem, we will follow the prime factorization approach:

Step 1: Start with the smallest prime number, which is 2.
Step 2: Divide 16 by 2 to get 8. Thus, $2 \cdot 8 = 16$ .
Step 3: Divide 8 by 2 to get 4. Thus, $2 \cdot 4 = 8$ .
Step 4: Divide 4 by 2 to get 2. Thus, $2 \cdot 2 = 4$ .
Step 5: Divide 2 by 2 to get 1. Thus, $2 \cdot 1 = 2$ .

After performing all divisions, the complete list of prime factors becomes $2, 2, 2, 2$ .

Therefore, the prime factors of 16 are all twos: $2, 2, 2, 2$ .

Finally, based on the available choices, the correct choice is:

$2, 2, 2, 2$ .

Final Answer

$2,2,2,2$

Key Points to Remember

Essential concepts to master this topic

Definition: Prime factors are the basic prime building blocks of any number
Technique: Divide repeatedly by smallest prime: 16 ÷ 2 = 8, 8 ÷ 2 = 4
Check: Multiply all prime factors together: 2 × 2 × 2 × 2 = 16 ✓

Common Mistakes

Avoid these frequent errors

Confusing factors with prime factors
Don't list all factors like 1, 2, 4, 8, 16 = includes composite numbers! The question asks specifically for prime factors only. Always break down to the smallest prime numbers that multiply to give 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 factors and prime factors?

Factors are all numbers that divide evenly into 16: 1, 2, 4, 8, 16. Prime factors are only the prime numbers that multiply together to make 16: 2, 2, 2, 2.

Why do I need to write 2 four times instead of just 2⁴?

When listing prime factors, we write each one separately to show the complete breakdown. Writing $2^4$ is the exponential form, but the question asks for all individual prime factors.

How do I know when to stop dividing?

Keep dividing until you reach 1. When you can't divide by any prime number anymore (meaning you've reached 1), you're done with the factorization.

What if I start with a different prime number?

Always start with the smallest prime that divides your number. For even numbers like 16, start with 2. This ensures you find all prime factors systematically.

Can 1 be a prime factor?

No! The number 1 is not prime because it only has one factor (itself). Prime numbers must have exactly two factors: 1 and themselves.

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