List All Factors of the Number 4: A Fundamental Exercise

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

Factors are all numbers that divide evenly into 4: {1, 2, 4}. Prime factorization uses only prime numbers: $ 2 \times 2 $, so we write 2, 2.

Q: Why is the answer 2, 2 instead of just 2?

Because $ 4 = 2 \times 2 $! We need to show that the prime number 2 appears twice in the factorization. Each 2 is equally important in making 4.

Q: Is 1 considered a prime factor of 4?

No! The number 1 is not considered prime by mathematical definition. Prime numbers must have exactly two factors: 1 and themselves. Since 1 only has one factor (itself), it's not prime.

Q: How do I know if a number is prime?

A prime number has exactly two factors: 1 and itself. For example, 2 is prime because its only factors are 1 and 2. Numbers like 4, 6, 8 are composite because they have more than two factors.

Q: What if the number was bigger, like 12?

Same process! Find the prime factorization: $ 12 = 2 \times 2 \times 3 $, so you'd write 2, 2, 3. Always break down to the smallest prime factors.

Prime Factorization with Small Composite Numbers

Write all the factors of the following number: $4$

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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

00:03 The ones digit is 4, therefore 2 is definitely a prime factor

00:06 Divide by 2, and continue with the result to find the factors

00:09 And the result is a prime number, therefore it's a factor by itself

00:12 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: $4$

Step-by-step solution

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

Identify all the factors of the number 4.
Determine which of these factors are prime numbers.
Check the answer choices to find the one that corresponds to the prime factorization of 4.

Now, let's work through each step:
Step 1: To find the factors of 4, we consider pairs of numbers that multiply to 4, such as $1 \times 4$ and $2 \times 2$ .
Step 2: Among these factors, identify the prime numbers. The number 2 is the only prime factor, and it needs to be listed twice since $2 \times 2 = 4$ .
Step 3: Looking at the answer choices, the choice that corresponds to the prime factorization of 4 is $2, 2$ .

Therefore, the correct answer is $2, 2$ .

Final Answer

$2,2$

Key Points to Remember

Essential concepts to master this topic

Definition: Factors are numbers that divide evenly into a given number
Method: Find pairs like $1 \times 4$ and $2 \times 2$ that equal 4
Verification: Check that each factor multiplies to give the original number ✓

Common Mistakes

Avoid these frequent errors

Listing all factors instead of prime factors only
Don't list factors like 1, 2, 4 when asked for prime factorization = wrong format! The question asks for prime factors, not all factors. Always identify which factors are prime numbers and list them according to their frequency in the factorization.

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 factorization?

Factors are all numbers that divide evenly into 4: {1, 2, 4}. Prime factorization uses only prime numbers: $2 \times 2$ , so we write 2, 2.

Why is the answer 2, 2 instead of just 2?

Because $4 = 2 \times 2$ ! We need to show that the prime number 2 appears twice in the factorization. Each 2 is equally important in making 4.

Is 1 considered a prime factor of 4?

No! The number 1 is not considered prime by mathematical definition. Prime numbers must have exactly two factors: 1 and themselves. Since 1 only has one factor (itself), it's not prime.

How do I know if a number is prime?

A prime number has exactly two factors: 1 and itself. For example, 2 is prime because its only factors are 1 and 2. Numbers like 4, 6, 8 are composite because they have more than two factors.

What if the number was bigger, like 12?

Same process! Find the prime factorization: $12 = 2 \times 2 \times 3$ , so you'd write 2, 2, 3. Always break down to the smallest prime factors.

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